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strict';\nvar ctx = require('./_ctx');\nvar $export = require('./_export');\nvar toObject = require('./_to-object');\nvar call = require('./_iter-call');\nvar isArrayIter = require('./_is-array-iter');\nvar toLength = require('./_to-length');\nvar createProperty = require('./_create-property');\nvar getIterFn = require('./core.get-iterator-method');\n\n$export($export.S + $export.F * !require('./_iter-detect')(function (iter) { Array.from(iter); }), 'Array', {\n  // 22.1.2.1 Array.from(arrayLike, mapfn = undefined, thisArg = undefined)\n  from: function from(arrayLike /* , mapfn = undefined, thisArg = undefined */) {\n    var O = toObject(arrayLike);\n    var C = typeof this == 'function' ? this : Array;\n    var aLen = arguments.length;\n    var mapfn = aLen > 1 ? arguments[1] : undefined;\n    var mapping = mapfn !== undefined;\n    var index = 0;\n    var iterFn = getIterFn(O);\n    var length, result, step, iterator;\n    if (mapping) mapfn = ctx(mapfn, aLen > 2 ? arguments[2] : undefined, 2);\n    // if object isn't iterable or it's array with default iterator - use simple case\n    if (iterFn != undefined && !(C == Array && isArrayIter(iterFn))) {\n      for (iterator = iterFn.call(O), result = new C(); !(step = iterator.next()).done; index++) {\n        createProperty(result, index, mapping ? call(iterator, mapfn, [step.value, index], true) : step.value);\n      }\n    } else {\n      length = toLength(O.length);\n      for (result = new C(length); length > index; index++) {\n        createProperty(result, index, mapping ? mapfn(O[index], index) : O[index]);\n      }\n    }\n    result.length = index;\n    return result;\n  }\n});\n","// 22.1.2.2 / 15.4.3.2 Array.isArray(arg)\nvar $export = require('./_export');\n\n$export($export.S, 'Array', { isArray: require('./_is-array') });\n","export * from \"-!../../node_modules/mini-css-extract-plugin/dist/loader.js??ref--8-oneOf-1-0!../../node_modules/css-loader/index.js??ref--8-oneOf-1-1!../../node_modules/vue-loader/lib/loaders/stylePostLoader.js!../../node_modules/postcss-loader/src/index.js??ref--8-oneOf-1-2!../../node_modules/sass-loader/dist/cjs.js??ref--8-oneOf-1-3!../../node_modules/cache-loader/dist/cjs.js??ref--0-0!../../node_modules/vue-loader/lib/index.js??vue-loader-options!./SubTopics.vue?vue&type=style&index=0&id=63f8118a&prod&scoped=true&lang=scss&\"","exports.f = require('./_wks');\n","// 21.2.5.3 get RegExp.prototype.flags()\nif (require('./_descriptors') && /./g.flags != 'g') require('./_object-dp').f(RegExp.prototype, 'flags', {\n  configurable: true,\n  get: require('./_flags')\n});\n","var global = require('./_global');\nvar core = require('./_core');\nvar LIBRARY = require('./_library');\nvar wksExt = require('./_wks-ext');\nvar defineProperty = require('./_object-dp').f;\nmodule.exports = function (name) {\n  var $Symbol = core.Symbol || (core.Symbol = LIBRARY ? {} : global.Symbol || {});\n  if (name.charAt(0) != '_' && !(name in $Symbol)) defineProperty($Symbol, name, { value: wksExt.f(name) });\n};\n","'use strict';\nrequire('./es6.regexp.flags');\nvar anObject = require('./_an-object');\nvar $flags = require('./_flags');\nvar DESCRIPTORS = require('./_descriptors');\nvar TO_STRING = 'toString';\nvar $toString = /./[TO_STRING];\n\nvar define = function (fn) {\n  require('./_redefine')(RegExp.prototype, TO_STRING, fn, true);\n};\n\n// 21.2.5.14 RegExp.prototype.toString()\nif (require('./_fails')(function () { return $toString.call({ source: 'a', flags: 'b' }) != '/a/b'; })) {\n  define(function toString() {\n    var R = anObject(this);\n    return '/'.concat(R.source, '/',\n      'flags' in R ? R.flags : !DESCRIPTORS && R instanceof RegExp ? $flags.call(R) : undefined);\n  });\n// FF44- RegExp#toString has a wrong name\n} else if ($toString.name != TO_STRING) {\n  define(function toString() {\n    return $toString.call(this);\n  });\n}\n","// fallback for IE11 buggy Object.getOwnPropertyNames with iframe and window\nvar toIObject = require('./_to-iobject');\nvar gOPN = require('./_object-gopn').f;\nvar toString = {}.toString;\n\nvar windowNames = typeof window == 'object' && window && Object.getOwnPropertyNames\n  ? Object.getOwnPropertyNames(window) : [];\n\nvar getWindowNames = function (it) {\n  try {\n    return gOPN(it);\n  } catch (e) {\n    return windowNames.slice();\n  }\n};\n\nmodule.exports.f = function getOwnPropertyNames(it) {\n  return windowNames && toString.call(it) == '[object Window]' ? getWindowNames(it) : gOPN(toIObject(it));\n};\n","var DateProto = Date.prototype;\nvar INVALID_DATE = 'Invalid Date';\nvar TO_STRING = 'toString';\nvar $toString = DateProto[TO_STRING];\nvar getTime = DateProto.getTime;\nif (new Date(NaN) + '' != INVALID_DATE) {\n  require('./_redefine')(DateProto, TO_STRING, function toString() {\n    var value = getTime.call(this);\n    // eslint-disable-next-line no-self-compare\n    return value === value ? $toString.call(this) : INVALID_DATE;\n  });\n}\n","'use strict';\n// ECMAScript 6 symbols shim\nvar global = require('./_global');\nvar has = require('./_has');\nvar DESCRIPTORS = require('./_descriptors');\nvar $export = require('./_export');\nvar redefine = require('./_redefine');\nvar META = require('./_meta').KEY;\nvar $fails = require('./_fails');\nvar shared = require('./_shared');\nvar setToStringTag = require('./_set-to-string-tag');\nvar uid = require('./_uid');\nvar wks = require('./_wks');\nvar wksExt = require('./_wks-ext');\nvar wksDefine = require('./_wks-define');\nvar enumKeys = require('./_enum-keys');\nvar isArray = require('./_is-array');\nvar anObject = require('./_an-object');\nvar isObject = require('./_is-object');\nvar toObject = require('./_to-object');\nvar toIObject = require('./_to-iobject');\nvar toPrimitive = require('./_to-primitive');\nvar createDesc = require('./_property-desc');\nvar _create = require('./_object-create');\nvar gOPNExt = require('./_object-gopn-ext');\nvar $GOPD = require('./_object-gopd');\nvar $GOPS = require('./_object-gops');\nvar $DP = require('./_object-dp');\nvar $keys = require('./_object-keys');\nvar gOPD = $GOPD.f;\nvar dP = $DP.f;\nvar gOPN = gOPNExt.f;\nvar $Symbol = global.Symbol;\nvar $JSON = global.JSON;\nvar _stringify = $JSON && $JSON.stringify;\nvar PROTOTYPE = 'prototype';\nvar HIDDEN = wks('_hidden');\nvar TO_PRIMITIVE = wks('toPrimitive');\nvar isEnum = {}.propertyIsEnumerable;\nvar SymbolRegistry = shared('symbol-registry');\nvar AllSymbols = shared('symbols');\nvar OPSymbols = shared('op-symbols');\nvar ObjectProto = Object[PROTOTYPE];\nvar USE_NATIVE = typeof $Symbol == 'function' && !!$GOPS.f;\nvar QObject = global.QObject;\n// Don't use setters in Qt Script, https://github.com/zloirock/core-js/issues/173\nvar setter = !QObject || !QObject[PROTOTYPE] || !QObject[PROTOTYPE].findChild;\n\n// fallback for old Android, https://code.google.com/p/v8/issues/detail?id=687\nvar setSymbolDesc = DESCRIPTORS && $fails(function () {\n  return _create(dP({}, 'a', {\n    get: function () { return dP(this, 'a', { value: 7 }).a; }\n  })).a != 7;\n}) ? function (it, key, D) {\n  var protoDesc = gOPD(ObjectProto, key);\n  if (protoDesc) delete ObjectProto[key];\n  dP(it, key, D);\n  if (protoDesc && it !== ObjectProto) dP(ObjectProto, key, protoDesc);\n} : dP;\n\nvar wrap = function (tag) {\n  var sym = AllSymbols[tag] = _create($Symbol[PROTOTYPE]);\n  sym._k = tag;\n  return sym;\n};\n\nvar isSymbol = USE_NATIVE && typeof $Symbol.iterator == 'symbol' ? function (it) {\n  return typeof it == 'symbol';\n} : function (it) {\n  return it instanceof $Symbol;\n};\n\nvar $defineProperty = function defineProperty(it, key, D) {\n  if (it === ObjectProto) $defineProperty(OPSymbols, key, D);\n  anObject(it);\n  key = toPrimitive(key, true);\n  anObject(D);\n  if (has(AllSymbols, key)) {\n    if (!D.enumerable) {\n      if (!has(it, HIDDEN)) dP(it, HIDDEN, createDesc(1, {}));\n      it[HIDDEN][key] = true;\n    } else {\n      if (has(it, HIDDEN) && it[HIDDEN][key]) it[HIDDEN][key] = false;\n      D = _create(D, { enumerable: createDesc(0, false) });\n    } return setSymbolDesc(it, key, D);\n  } return dP(it, key, D);\n};\nvar $defineProperties = function defineProperties(it, P) {\n  anObject(it);\n  var keys = enumKeys(P = toIObject(P));\n  var i = 0;\n  var l = keys.length;\n  var key;\n  while (l > i) $defineProperty(it, key = keys[i++], P[key]);\n  return it;\n};\nvar $create = function create(it, P) {\n  return P === undefined ? _create(it) : $defineProperties(_create(it), P);\n};\nvar $propertyIsEnumerable = function propertyIsEnumerable(key) {\n  var E = isEnum.call(this, key = toPrimitive(key, true));\n  if (this === ObjectProto && has(AllSymbols, key) && !has(OPSymbols, key)) return false;\n  return E || !has(this, key) || !has(AllSymbols, key) || has(this, HIDDEN) && this[HIDDEN][key] ? E : true;\n};\nvar $getOwnPropertyDescriptor = function getOwnPropertyDescriptor(it, key) {\n  it = toIObject(it);\n  key = toPrimitive(key, true);\n  if (it === ObjectProto && has(AllSymbols, key) && !has(OPSymbols, key)) return;\n  var D = gOPD(it, key);\n  if (D && has(AllSymbols, key) && !(has(it, HIDDEN) && it[HIDDEN][key])) D.enumerable = true;\n  return D;\n};\nvar $getOwnPropertyNames = function getOwnPropertyNames(it) {\n  var names = gOPN(toIObject(it));\n  var result = [];\n  var i = 0;\n  var key;\n  while (names.length > i) {\n    if (!has(AllSymbols, key = names[i++]) && key != HIDDEN && key != META) result.push(key);\n  } return result;\n};\nvar $getOwnPropertySymbols = function getOwnPropertySymbols(it) {\n  var IS_OP = it === ObjectProto;\n  var names = gOPN(IS_OP ? OPSymbols : toIObject(it));\n  var result = [];\n  var i = 0;\n  var key;\n  while (names.length > i) {\n    if (has(AllSymbols, key = names[i++]) && (IS_OP ? has(ObjectProto, key) : true)) result.push(AllSymbols[key]);\n  } return result;\n};\n\n// 19.4.1.1 Symbol([description])\nif (!USE_NATIVE) {\n  $Symbol = function Symbol() {\n    if (this instanceof $Symbol) throw TypeError('Symbol is not a constructor!');\n    var tag = uid(arguments.length > 0 ? arguments[0] : undefined);\n    var $set = function (value) {\n      if (this === ObjectProto) $set.call(OPSymbols, value);\n      if (has(this, HIDDEN) && has(this[HIDDEN], tag)) this[HIDDEN][tag] = false;\n      setSymbolDesc(this, tag, createDesc(1, value));\n    };\n    if (DESCRIPTORS && setter) setSymbolDesc(ObjectProto, tag, { configurable: true, set: $set });\n    return wrap(tag);\n  };\n  redefine($Symbol[PROTOTYPE], 'toString', function toString() {\n    return this._k;\n  });\n\n  $GOPD.f = $getOwnPropertyDescriptor;\n  $DP.f = $defineProperty;\n  require('./_object-gopn').f = gOPNExt.f = $getOwnPropertyNames;\n  require('./_object-pie').f = $propertyIsEnumerable;\n  $GOPS.f = $getOwnPropertySymbols;\n\n  if (DESCRIPTORS && !require('./_library')) {\n    redefine(ObjectProto, 'propertyIsEnumerable', $propertyIsEnumerable, true);\n  }\n\n  wksExt.f = function (name) {\n    return wrap(wks(name));\n  };\n}\n\n$export($export.G + $export.W + $export.F * !USE_NATIVE, { Symbol: $Symbol });\n\nfor (var es6Symbols = (\n  // 19.4.2.2, 19.4.2.3, 19.4.2.4, 19.4.2.6, 19.4.2.8, 19.4.2.9, 19.4.2.10, 19.4.2.11, 19.4.2.12, 19.4.2.13, 19.4.2.14\n  'hasInstance,isConcatSpreadable,iterator,match,replace,search,species,split,toPrimitive,toStringTag,unscopables'\n).split(','), j = 0; es6Symbols.length > j;)wks(es6Symbols[j++]);\n\nfor (var wellKnownSymbols = $keys(wks.store), k = 0; wellKnownSymbols.length > k;) wksDefine(wellKnownSymbols[k++]);\n\n$export($export.S + $export.F * !USE_NATIVE, 'Symbol', {\n  // 19.4.2.1 Symbol.for(key)\n  'for': function (key) {\n    return has(SymbolRegistry, key += '')\n      ? SymbolRegistry[key]\n      : SymbolRegistry[key] = $Symbol(key);\n  },\n  // 19.4.2.5 Symbol.keyFor(sym)\n  keyFor: function keyFor(sym) {\n    if (!isSymbol(sym)) throw TypeError(sym + ' is not a symbol!');\n    for (var key in SymbolRegistry) if (SymbolRegistry[key] === sym) return key;\n  },\n  useSetter: function () { setter = true; },\n  useSimple: function () { setter = false; }\n});\n\n$export($export.S + $export.F * !USE_NATIVE, 'Object', {\n  // 19.1.2.2 Object.create(O [, Properties])\n  create: $create,\n  // 19.1.2.4 Object.defineProperty(O, P, Attributes)\n  defineProperty: $defineProperty,\n  // 19.1.2.3 Object.defineProperties(O, Properties)\n  defineProperties: $defineProperties,\n  // 19.1.2.6 Object.getOwnPropertyDescriptor(O, P)\n  getOwnPropertyDescriptor: $getOwnPropertyDescriptor,\n  // 19.1.2.7 Object.getOwnPropertyNames(O)\n  getOwnPropertyNames: $getOwnPropertyNames,\n  // 19.1.2.8 Object.getOwnPropertySymbols(O)\n  getOwnPropertySymbols: $getOwnPropertySymbols\n});\n\n// Chrome 38 and 39 `Object.getOwnPropertySymbols` fails on primitives\n// https://bugs.chromium.org/p/v8/issues/detail?id=3443\nvar FAILS_ON_PRIMITIVES = $fails(function () { $GOPS.f(1); });\n\n$export($export.S + $export.F * FAILS_ON_PRIMITIVES, 'Object', {\n  getOwnPropertySymbols: function getOwnPropertySymbols(it) {\n    return $GOPS.f(toObject(it));\n  }\n});\n\n// 24.3.2 JSON.stringify(value [, replacer [, space]])\n$JSON && $export($export.S + $export.F * (!USE_NATIVE || $fails(function () {\n  var S = $Symbol();\n  // MS Edge converts symbol values to JSON as {}\n  // WebKit converts symbol values to JSON as null\n  // V8 throws on boxed symbols\n  return _stringify([S]) != '[null]' || _stringify({ a: S }) != '{}' || _stringify(Object(S)) != '{}';\n})), 'JSON', {\n  stringify: function stringify(it) {\n    var args = [it];\n    var i = 1;\n    var replacer, $replacer;\n    while (arguments.length > i) args.push(arguments[i++]);\n    $replacer = replacer = args[1];\n    if (!isObject(replacer) && it === undefined || isSymbol(it)) return; // IE8 returns string on undefined\n    if (!isArray(replacer)) replacer = function (key, value) {\n      if (typeof $replacer == 'function') value = $replacer.call(this, key, value);\n      if (!isSymbol(value)) return value;\n    };\n    args[1] = replacer;\n    return _stringify.apply($JSON, args);\n  }\n});\n\n// 19.4.3.4 Symbol.prototype[@@toPrimitive](hint)\n$Symbol[PROTOTYPE][TO_PRIMITIVE] || require('./_hide')($Symbol[PROTOTYPE], TO_PRIMITIVE, $Symbol[PROTOTYPE].valueOf);\n// 19.4.3.5 Symbol.prototype[@@toStringTag]\nsetToStringTag($Symbol, 'Symbol');\n// 20.2.1.9 Math[@@toStringTag]\nsetToStringTag(Math, 'Math', true);\n// 24.3.3 JSON[@@toStringTag]\nsetToStringTag(global.JSON, 'JSON', true);\n","require('./_wks-define')('asyncIterator');\n","var render = function render(){var _vm=this,_c=_vm._self._c;return _c('div',[_c('div',{staticClass:\"font-weight-medium\",class:{'display-1': _vm.$vuetify.breakpoint.lgAndUp,'headline': _vm.$vuetify.breakpoint.mdOnly, 'subheading': _vm.$vuetify.breakpoint.smAndDown}},[_c('span',{staticStyle:{\"font-family\":\"Oswald\"}},[_vm._v(\"Introduction\")])]),_c('div',{staticStyle:{\"margin-top\":\"10px\"}}),_c('v-layout',{attrs:{\"align-center\":\"\",\"justify-center\":\"\",\"row\":\"\",\"wrap\":\"\"}},[_c('v-flex',{staticClass:\"subheader-content font-weight-light\",class:{'headline': _vm.$vuetify.breakpoint.lgAndUp,'body-2': _vm.$vuetify.breakpoint.mdOnly, 'body-2': _vm.$vuetify.breakpoint.smAndDown},attrs:{\"xs12\":\"\",\"sm8\":\"\",\"md8\":\"\",\"lg8\":\"\",\"xl8\":\"\"}},[_vm._v(\"\\n      A matrix is a collection of numbers arranged in a table with a given number\\n      of rows and columns. Matrices must have the same number of elements in each\\n      row or column (no jagged edges).\\n      The following examples are matrices:\\n\\n      $$\\n      \\\\mathbf{A} = \\\\begin{bmatrix}\\n      1 & 10 & -1 \\\\\\\\\\n      3 & 0 & 34 \\\\\\\\\\n      1 & 1 & 4 \\\\\\\\\\n      -2 & 2 & 1.5 \\\\\\\\\\n      \\\\end{bmatrix}\\n      \\\\qquad\\n      \\\\mathbf{B} = \\\\begin{bmatrix}\\n      1 & -1 \\\\\\\\\\n      2 & 1 \\\\\\\\\\n      \\\\end{bmatrix}\\n      $$\\n\\n      These are not matices, since they are missing elements in some rows or columns:\\n\\n      $$\\n      \\\\mathbf{C} = \\\\begin{bmatrix}\\n      6 &   \\\\\\\\\\n      2 & 7 \\\\\\\\\\n      \\\\end{bmatrix}\\n      \\\\qquad\\n      \\\\mathbf{D} = \\\\begin{bmatrix}\\n      -1 & 2 & 3 \\\\\\\\\\n      & 5 & 6 \\\\\\\\\\n      \\\\end{bmatrix}\\n      $$\\n\\n      You can perform operations like addition, subtraction, and multiplication\\n      on matrices much like with regular numbers, but special rules must be followed.\\n      In this lesson, you will learn how to perform these operations on matrices.\\n      \"),_c('br'),_c('div',{staticStyle:{\"margin-top\":\"20px\"}}),_c('div',{staticClass:\"font-weight-medium\",class:{'display-1': _vm.$vuetify.breakpoint.lgAndUp,'headline': _vm.$vuetify.breakpoint.mdOnly, 'subheading': _vm.$vuetify.breakpoint.smAndDown}},[_c('span',{staticStyle:{\"font-family\":\"Oswald\"}},[_vm._v(\" Outline\")])]),_c('div',{staticStyle:{\"margin-top\":\"10px\"}}),_vm._v(\"\\n      This chapter on matrices consists of three lessons. Each lesson comes with an interactive MagicGraph that offers students a uniquely engaging and effective learning experience.\\n      \"),_c('h5',[_vm._v(\"Lesson 1\")]),_vm._v(\"\\n      Matrix Components: How do you talk about the values in a matrix?\\n      \"),_c('h5',[_vm._v(\"Lesson 2\")]),_vm._v(\"\\n      Matrix Addition: How do you add two matrices together?\\n      \"),_c('h5',[_vm._v(\"Lesson 3\")]),_vm._v(\"\\n      Matrix Multiplication: When are you allowed to multiply matrices, and how do you do it?\\n      \"),_c('br'),_c('br')]),_c('v-flex',{attrs:{\"xs12\":\"\",\"sm4\":\"\",\"md4\":\"\",\"lg4\":\"\",\"xl4\":\"\"}},[_c('h5',{staticStyle:{\"text-align\":\"center\"}},[_vm._v(\"\\n        Matrices are used in almost every branch of mathematical and scientific discipline. The great theoretical physicist Albert Einstein derived the fundamental equations of Special and General Relativity using matrices.\\n      \")]),_c('v-img',{staticClass:\"imgC\",attrs:{\"padding\":\"0px\",\"max-height\":\"500px\",\"max-width\":\"500px\",\"src\":\"/assets/einstein.jpg\",\"contain\":\"\"}})],1)],1),_c('div',{staticClass:\"font-weight-medium\",class:{'display-1': _vm.$vuetify.breakpoint.lgAndUp,'headline': _vm.$vuetify.breakpoint.mdOnly, 'subheading': _vm.$vuetify.breakpoint.smAndDown}},[_c('span',{staticStyle:{\"font-family\":\"Oswald\"}},[_vm._v(\"Let's get started\")])]),_c('div',{staticStyle:{\"margin-top\":\"10px\"}}),_c('div',{staticClass:\"subheader-content font-weight-light\",class:{'headline': _vm.$vuetify.breakpoint.lgAndUp,'body-2': _vm.$vuetify.breakpoint.mdOnly, 'body-2': _vm.$vuetify.breakpoint.smAndDown}},[_vm._v(\"\\n    Explore our comprehensive library of interactive lessons on matrices.\\n  \")]),_c('div',{staticStyle:{\"margin-top\":\"20px\"}}),_c('v-container',{attrs:{\"grid-list-xl\":\"\",\"text-xs-center\":\"\"}},[_c('v-layout',{attrs:{\"align-center\":\"\",\"justify-center\":\"\",\"row\":\"\"}},_vm._l((_vm.topics),function(topic){return _c('v-flex',{key:topic.key,attrs:{\"xs12\":\"\",\"sm12\":\"\",\"md12\":\"\",\"lg12\":\"\",\"xl12\":\"\"}},[_c('subtopic-card',{attrs:{\"headline\":topic.headline,\"description\":topic.description,\"img\":topic.img,\"path\":topic.path}})],1)}),1)],1),_c('br'),_c('br'),_c('br')],1)\n}\nvar staticRenderFns = []\n\nexport { render, staticRenderFns }","<template>\r\n  <div>\r\n    <div class=\"font-weight-medium\"\r\n         :class=\"{'display-1': $vuetify.breakpoint.lgAndUp,'headline': $vuetify.breakpoint.mdOnly, 'subheading': $vuetify.breakpoint.smAndDown}\"\r\n    >\r\n      <span style=\"font-family:Oswald\">Introduction</span>\r\n    </div>\r\n    <div style=\"margin-top: 10px\" />\r\n    <v-layout align-center\n              justify-center\n              row\n              wrap\n    >\r\n      <v-flex xs12\n              sm8\n              md8\n              lg8\n              xl8\r\n              class=\"subheader-content font-weight-light\"\r\n              :class=\"{'headline': $vuetify.breakpoint.lgAndUp,'body-2': $vuetify.breakpoint.mdOnly, 'body-2': $vuetify.breakpoint.smAndDown}\"\r\n      >\r\n        A matrix is a collection of numbers arranged in a table with a given number\r\n        of rows and columns. Matrices must have the same number of elements in each\r\n        row or column (no jagged edges).\r\n        The following examples are matrices:\r\n\r\n        $$\r\n        \\mathbf{A} = \\begin{bmatrix}\r\n        1 & 10 & -1 \\\\\r\n        3 & 0 & 34 \\\\\r\n        1 & 1 & 4 \\\\\r\n        -2 & 2 & 1.5 \\\\\r\n        \\end{bmatrix}\r\n        \\qquad\r\n        \\mathbf{B} = \\begin{bmatrix}\r\n        1 & -1 \\\\\r\n        2 & 1 \\\\\r\n        \\end{bmatrix}\r\n        $$\r\n\r\n        These are not matices, since they are missing elements in some rows or columns:\r\n\r\n        $$\r\n        \\mathbf{C} = \\begin{bmatrix}\r\n        6 &   \\\\\r\n        2 & 7 \\\\\r\n        \\end{bmatrix}\r\n        \\qquad\r\n        \\mathbf{D} = \\begin{bmatrix}\r\n        -1 & 2 & 3 \\\\\r\n        & 5 & 6 \\\\\r\n        \\end{bmatrix}\r\n        $$\r\n\r\n        You can perform operations like addition, subtraction, and multiplication\r\n        on matrices much like with regular numbers, but special rules must be followed.\r\n        In this lesson, you will learn how to perform these operations on matrices.\r\n        <br>\r\n        <div style=\"margin-top: 20px\" />\r\n        <div class=\"font-weight-medium\"\r\n             :class=\"{'display-1': $vuetify.breakpoint.lgAndUp,'headline': $vuetify.breakpoint.mdOnly, 'subheading': $vuetify.breakpoint.smAndDown}\"\r\n        >\r\n          <span style=\"font-family:Oswald\"> Outline</span>\r\n        </div>\r\n        <div style=\"margin-top: 10px\" />\r\n        This chapter on matrices consists of three lessons. Each lesson comes with an interactive MagicGraph that offers students a uniquely engaging and effective learning experience.\r\n        <h5>Lesson 1</h5>\r\n        Matrix Components: How do you talk about the values in a matrix?\r\n        <h5>Lesson 2</h5>\r\n        Matrix Addition: How do you add two matrices together?\r\n        <h5>Lesson 3</h5>\r\n        Matrix Multiplication: When are you allowed to multiply matrices, and how do you do it?\r\n        <br>\r\n        <br>\r\n      </v-flex>\r\n      <v-flex xs12\n              sm4\n              md4\n              lg4\n              xl4\n      >\r\n        <h5 style=\"text-align:center\">\r\n          Matrices are used in almost every branch of mathematical and scientific discipline. The great theoretical physicist Albert Einstein derived the fundamental equations of Special and General Relativity using matrices.\r\n        </h5>\r\n        <v-img class=\"imgC\"\r\n               padding=\"0px\"\r\n               max-height=\"500px\"\r\n               max-width=\"500px\"\r\n               src=\"/assets/einstein.jpg\"\r\n               contain\r\n        />\r\n      </v-flex>\r\n    </v-layout>\r\n    <div class=\"font-weight-medium\"\r\n         :class=\"{'display-1': $vuetify.breakpoint.lgAndUp,'headline': $vuetify.breakpoint.mdOnly, 'subheading': $vuetify.breakpoint.smAndDown}\"\r\n    >\r\n      <span style=\"font-family:Oswald\">Let's get started</span>\r\n    </div>\r\n    <div style=\"margin-top: 10px\" />\r\n    <div class=\"subheader-content font-weight-light\"\r\n         :class=\"{'headline': $vuetify.breakpoint.lgAndUp,'body-2': $vuetify.breakpoint.mdOnly, 'body-2': $vuetify.breakpoint.smAndDown}\"\r\n    >\r\n      Explore our comprehensive library of interactive lessons on matrices.\r\n    </div>\r\n    <div style=\"margin-top: 20px\" />\r\n    <v-container grid-list-xl text-xs-center>\r\n      <v-layout\r\n        align-center\r\n        justify-center\r\n        row\r\n      >\r\n        <v-flex v-for=\"topic in topics\"\r\n                :key=\"topic.key\"\r\n                xs12\r\n                sm12\r\n                md12\r\n                lg12\r\n                xl12\r\n        >\r\n          <subtopic-card\r\n            :headline=\"topic.headline\"\r\n            :description=\"topic.description\"\r\n            :img=\"topic.img\"\r\n            :path=\"topic.path\"\r\n          />\r\n        </v-flex>\r\n      </v-layout>\r\n    </v-container>\r\n    <br>\r\n    <br>\r\n    <br>\r\n  </div>\r\n</template>\r\n<script>\r\nimport SubtopicCard from '../../../views/SubTopics.vue'\r\nexport default {\r\n    name: 'Matrices',\r\n    components: {\r\n    SubtopicCard\r\n    },\r\n    data () {\r\n      return {\r\n        playerOptions: {\r\n          preload:'auto',\r\n          ratio: '16:9'\r\n        },\r\n        topics: [\r\n          {\r\n            headline:    \"Matrix Components\",\r\n            description: \"How do you talk about the values in a matrix?\",\r\n            img:         \"/assets/wdice-1.svg\",\r\n            path:        \"/mathematics/matrices/components\",\r\n          },\r\n          {\r\n            headline:    \"Matrix Addition\",\r\n            description: \"Learn when you can add two matrices together and practice it!\",\r\n            img:         \"/assets/wdice-2.svg\",\r\n            path:        \"/mathematics/matrices/addition\",\r\n          },\r\n          {\r\n            headline:    \"Matrix Multiplication\",\r\n            description: \"Matrices can also be multiplied together -- learn how to do it here!\",\r\n            img:         \"/assets/wdice-3.svg\",\r\n            path:        \"/mathematics/matrices/multiplication\",\r\n          },\r\n          {\r\n            headline:    \"Determinant\",\r\n            description: \"Matrices can also be multiplied together -- learn how to do it here!\",\r\n            img:         \"/assets/wdice-4.svg\",\r\n            path:        \"/comingsoon\",\r\n          },\r\n        ]\r\n    }\r\n  },\r\n    created () {\r\n      this.$store.commit('navigation/resetState');\r\n      const title = 'Matrices';\r\n      this.$store.commit('navigation/changeTitle', title);\r\n      this.$store.commit('navigation/changeMenu', title);\r\n\r\n      // Remap data in our topics section to something that can be used for the\r\n      // side menu. This makes sure there's only one source of data we need to\r\n      // update.\r\n      let newTopics = [];\r\n      for (const topic of this.topics) {\r\n        let newTopic = topic;\r\n        newTopic['action'] = () => this.$router.push({path: topic['path']});\r\n        newTopic['title']  = topic['headline'];\r\n        newTopics.push(newTopic)\r\n      }\r\n\r\n      this.$store.commit('navigation/replaceTopics', newTopics);\r\n      let newshowhome = false;\r\n      this.$store.commit('navigation/toggleshowhome', newshowhome);\r\n      let newMath =true;\r\n      this.$store.commit('navigation/replaceMath', newMath);\r\n      let newLeftArrow =true;\r\n      this.$store.commit('navigation/replaceLeftArrow', newLeftArrow);\r\n      let newModule=true;\r\n      this.$store.commit('navigation/replaceModule', newModule);\r\n    },\r\n    mounted () {\r\n      MathJax.Hub.Queue([\"Typeset\", MathJax.Hub]);\r\n    },\r\n    metaInfo() {\r\n    return{ title: 'Matrices',\r\n            titleTemplate: '%s - Learn interactively',\r\n            meta: [ {name: 'viewport', content: 'width=device-width, initial-scale=1'},\r\n                    {name: 'description', content: 'Learn interactively about matrices.'}\r\n                  ]\r\n          }\r\n     }\r\n}\r\n</script>\r\n\r\n<style scoped lang=\"scss\">\r\n</style>\r\n","import mod from \"-!../../../../node_modules/cache-loader/dist/cjs.js??ref--12-0!../../../../node_modules/thread-loader/dist/cjs.js!../../../../node_modules/babel-loader/lib/index.js!../../../../node_modules/cache-loader/dist/cjs.js??ref--0-0!../../../../node_modules/vue-loader/lib/index.js??vue-loader-options!./Lesson.vue?vue&type=script&lang=js&\"; export default mod; export * from \"-!../../../../node_modules/cache-loader/dist/cjs.js??ref--12-0!../../../../node_modules/thread-loader/dist/cjs.js!../../../../node_modules/babel-loader/lib/index.js!../../../../node_modules/cache-loader/dist/cjs.js??ref--0-0!../../../../node_modules/vue-loader/lib/index.js??vue-loader-options!./Lesson.vue?vue&type=script&lang=js&\"","import { render, staticRenderFns } from \"./Lesson.vue?vue&type=template&id=d6ce0e3c&scoped=true&\"\nimport script from \"./Lesson.vue?vue&type=script&lang=js&\"\nexport * from \"./Lesson.vue?vue&type=script&lang=js&\"\n\n\n/* normalize component */\nimport normalizer from \"!../../../../node_modules/vue-loader/lib/runtime/componentNormalizer.js\"\nvar component = normalizer(\n  script,\n  render,\n  staticRenderFns,\n  false,\n  null,\n  \"d6ce0e3c\",\n  null\n  \n)\n\nexport default component.exports","// all enumerable object keys, includes symbols\nvar getKeys = require('./_object-keys');\nvar gOPS = require('./_object-gops');\nvar pIE = require('./_object-pie');\nmodule.exports = function (it) {\n  var result = getKeys(it);\n  var getSymbols = gOPS.f;\n  if (getSymbols) {\n    var symbols = getSymbols(it);\n    var isEnum = pIE.f;\n    var i = 0;\n    var key;\n    while (symbols.length > i) if (isEnum.call(it, key = symbols[i++])) result.push(key);\n  } return result;\n};\n","var render = function render(){var _vm=this,_c=_vm._self._c;return _c('router-link',{attrs:{\"to\":_vm.path}},[_c('v-container',{staticStyle:{\"padding\":\"0px\"},attrs:{\"grid-list-xs\":\"\",\"fluid\":\"\"}},[_c('v-layout',{staticClass:\"px-1\",attrs:{\"align-center\":\"\",\"justify-center\":\"\",\"row\":\"\"}},[_c('v-hover',{scopedSlots:_vm._u([{key:\"default\",fn:function({ hover }){return [_c('v-card',{staticClass:\"rounded-card\",attrs:{\"elevation\":hover ? 9:2,\"height\":\"auto\",\"max-width\":\"400px\",\"align\":\"center\",\"justify\":\"center\",\"contain\":\"\"}},[_c('h3',{staticClass:\"font-weight-bold mt-3 text-center\",staticStyle:{\"color\":\"black\"}},[_vm._v(\"\\n            \"+_vm._s(_vm.headline)+\"\\n          \")]),_c('h4',{staticClass:\"font-weight-bold mt-2 text-center\",staticStyle:{\"color\":\"black\"}},[_vm._v(\"\\n            \"+_vm._s(_vm.description)+\"\\n          \")]),_c('v-divider',{staticClass:\"mt-3\",staticStyle:{\"color\":\"black\"}}),_c('v-img',{staticClass:\"mt-2 mb-2\",attrs:{\"src\":_vm.img,\"contain\":\"\"}})],1)]}}])})],1)],1)],1)\n}\nvar staticRenderFns = []\n\nexport { render, staticRenderFns }","<template>\r\n  <router-link :to=\"path\">\r\n    <v-container style=\"padding:0px\" grid-list-xs fluid>\r\n      <v-layout\r\n        align-center\r\n        justify-center\r\n        row\r\n        class=\"px-1\"\r\n      >\r\n        <v-hover v-slot:default=\"{ hover }\">\r\n          <v-card class=\"rounded-card\"\r\n                  :elevation=\"hover ? 9:2\"\r\n                  height=\"auto\"\r\n                  max-width=\"400px\"\r\n                  align=\"center\"\r\n                  justify=\"center\"\r\n                  contain\r\n          >\r\n            <h3 style=\"color:black;\" class=\" font-weight-bold mt-3 text-center\">\r\n              {{ headline }}\r\n            </h3>\r\n            <h4 style=\"color:black;\" class=\" font-weight-bold mt-2 text-center\">\r\n              {{ description }}\r\n            </h4>\r\n            <v-divider style=\"color:black;\" class=\"mt-3\" />\r\n            <v-img\r\n              class=\"mt-2 mb-2\"\r\n              :src=\"img\"\r\n              contain\r\n            />\r\n          </v-card>\r\n        </v-hover>\r\n      </v-layout>\r\n    </v-container>\r\n  </router-link>\r\n</template>\r\n<script>\r\nexport default {\r\n  props: {\r\n    headline: {\r\n      type: String,\r\n      default: '',\r\n      required: true\r\n    },\r\n    description: {\r\n      type: String,\r\n      default: '',\r\n      required: false\r\n    },\r\n    img: {\r\n      type: String,\r\n      default: '',\r\n      required: false\r\n    },\r\n    path: {\r\n      type: String,\r\n      default: '',\r\n      required: true\r\n    },\r\n  }\r\n}\r\n</script>\r\n<style scoped lang=\"scss\">\r\n@import '@/styles/screen-sizes.scss';\r\n.rounded-card {\r\n  margin-top:auto;\r\n  margin-bottom:auto;\r\n  @include respond-to(less-smallest-screens) {height:52vw; width:30vw; border-radius: 4.5px; }\r\n  @include respond-to(smallest-screens) { height:40vw; width:28vw; border-radius: 4.5px; }\r\n  @include respond-to(small-screens) { height:44vw; width:29vw;border-radius: 5.5px;}\r\n  @include respond-to(medium-screens) { height:42vw; width:28vw;border-radius: 6.5px;}\r\n  @include respond-to(large-screens) { height: 32vw; width:22vw;border-radius: 7.5px;}\r\n  @include respond-to(largest-screens) { height:auto; width:15vw; border-radius: 8.5px;}\r\n}\r\n.thumbnail {\r\n  display: inline-block;\r\n  max-width: 100%; /* only this one important */\r\n  margin-bottom: 1rem;\r\n  border: solid 4px #fefefe;\r\n  border-radius: 3px;\r\n  box-shadow: 0 0 0 1px rgba(10, 10, 10, 0.2);\r\n  line-height: 0; }\r\n.imgC{\r\n  justify:center;\r\n  align:center;\r\n  position:relative;\r\n  @include respond-to(less-smallest-screens) {height:60px; top:5px;}\r\n  @include respond-to(smallest-screens) {height:60px;top:6.5px;}\r\n  @include respond-to(small-screens) {height:70px;top:10px;}\r\n  @include respond-to(medium-screens) {height:80px;top:12px;}\r\n  @include respond-to(large-screens) {height: 140px;top:12px;}\r\n  @include respond-to(largest-screens) {height:150px;top:15px;}\r\n  padding-bottom:20px;\r\n  padding-top:30px;\r\n  }\r\n.subjects{\r\n  text-decoration: none;\r\n  font-family: Oswald;\r\n  display: inline-block;\r\n  text-align:center;\r\n  position:relative;\r\n  @include respond-to(less-smallest-screens) {font-size:2vw;padding-top:15px}\r\n  @include respond-to(smallest-screens) {font-size:2vw;padding-top:15px}\r\n  @include respond-to(small-screens) {font-size:3vw;padding-top:20px;}\r\n  @include respond-to(medium-screens) {font-size:2.0vw;padding-top:15px;}\r\n  @include respond-to(large-screens) {font-size:2.0vw;padding-top:15px;}\r\n  @include respond-to(largest-screens) {font-size:2.0vw; padding-top:20px;}\r\n  }\r\na {\r\n  text-decoration: none !important;\r\n}\r\n\r\n</style>\r\n","import mod from \"-!../../node_modules/cache-loader/dist/cjs.js??ref--12-0!../../node_modules/thread-loader/dist/cjs.js!../../node_modules/babel-loader/lib/index.js!../../node_modules/cache-loader/dist/cjs.js??ref--0-0!../../node_modules/vue-loader/lib/index.js??vue-loader-options!./SubTopics.vue?vue&type=script&lang=js&\"; export default mod; export * from \"-!../../node_modules/cache-loader/dist/cjs.js??ref--12-0!../../node_modules/thread-loader/dist/cjs.js!../../node_modules/babel-loader/lib/index.js!../../node_modules/cache-loader/dist/cjs.js??ref--0-0!../../node_modules/vue-loader/lib/index.js??vue-loader-options!./SubTopics.vue?vue&type=script&lang=js&\"","import { render, staticRenderFns } from \"./SubTopics.vue?vue&type=template&id=63f8118a&scoped=true&\"\nimport script from \"./SubTopics.vue?vue&type=script&lang=js&\"\nexport * from \"./SubTopics.vue?vue&type=script&lang=js&\"\nimport style0 from \"./SubTopics.vue?vue&type=style&index=0&id=63f8118a&prod&scoped=true&lang=scss&\"\n\n\n/* normalize component */\nimport normalizer from \"!../../node_modules/vue-loader/lib/runtime/componentNormalizer.js\"\nvar component = normalizer(\n  script,\n  render,\n  staticRenderFns,\n  false,\n  null,\n  \"63f8118a\",\n  null\n  \n)\n\nexport default component.exports"],"sourceRoot":""}