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Matrix multiplication
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<iframe 
    src="https://jsxgraph.org/share/iframe/matrix-multiplication" 
    style="border: 1px solid black; overflow: hidden; width: 550px; aspect-ratio: 55 / 65;" 
    name="JSXGraph example: Matrix multiplication" 
    allowfullscreen
></iframe>
This code has to 
<div id="board-0-wrapper" class="jxgbox-wrapper " style="width: 100%; ">
   <div id="board-0" class="jxgbox" style="aspect-ratio: 1 / 1; width: 75%;" data-ar="1 / 1"></div>
</div>
<div id="board-1-wrapper" class="jxgbox-wrapper " style="width: 100%; ">
   <div id="board-1" class="jxgbox" style="aspect-ratio: 1 / 1; width: 75%;" data-ar="1 / 1"></div>
</div>

<script type = "text/javascript"> 
    /*
    This example is licensed under a 
    Creative Commons Attribution ShareAlike 4.0 International License.
    https://creativecommons.org/licenses/by-sa/4.0/
    
    Please note you have to mention 
    The Center of Mobile Learning with Digital Technology
    in the credits.
    */
    
    const BOARDID0 = 'board-0';
    const BOARDID1 = 'board-1';
    const BOARDID = BOARDID0;

      var board1 = JXG.JSXGraph.initBoard(BOARDID0, { boundingbox: [-7.5, 7.5, 12.5, -7.5], axis: true });
      var a = board1.create('slider', [[-5, -2], [5, -2], [-5, 1, 5]], { name: 'a', snapWidth: 0.1 });
      var b = board1.create('slider', [[-5, -3], [5, -3], [-5, 0, 5]], { name: 'b', snapWidth: 0.1 });
      var c = board1.create('slider', [[-5, -4], [5, -4], [-5, 0, 5]], { name: 'c', snapWidth: 0.1 });
      var d = board1.create('slider', [[-5, -5], [5, -5], [-5, 1, 5]], { name: 'd', snapWidth: 0.1 });
    
      var v = board1.create('point', [2, 2], { size: 3, name: 'v' });
      var w = board1.create('point', [-2, 1], { size: 3, name: 'w' });
      var va = board1.create('arrow', [[0, 0], v]);
      var wa = board1.create('arrow', [[0, 0], w]);
    
      var board2 = JXG.JSXGraph.initBoard(BOARDID1, { boundingbox: [-7.5, 7.5, 12.5, -7.5], axis: true });
      board1.addChild(board2);
    
      var v2 = board2.create('point', [
           () => a.Value() * v.X() + b.Value() * v.Y(),
           () => c.Value() * v.X() + d.Value() * v.Y()], 
           { face: '[]', size: 2, name: "v'" });
      var w2 = board2.create('point', [
           () => a.Value() * w.X() + b.Value() * w.Y(),
           () => c.Value() * w.X() + d.Value() * w.Y()], 
           { face: '[]', size: 2, name: "w'" });
      var va2 = board2.create('segment', [[0, 0], v2], { lastArrow: true });
      var wa2 = board2.create('segment', [[0, 0], w2], { lastArrow: true });
      
      board2.create('text', [-6, -2, () => '|' + (a.Value()).toFixed(2) + ' ' + (b.Value()).toFixed(2) +
              '|' + '<br>' + '|' + (c.Value()).toFixed(2) + ' ' + (d.Value()).toFixed(2) + '|']);
    
      // board2.create('text', [-6, 5, function() { return '\\begin{pmatrix}' + (a.Value()).toFixed(2) + ' &' + (b.Value()).toFixed(2) + '\\\\' +
      //        (c.Value()).toFixed(2) + '& ' + (d.Value()).toFixed(2) + '\\end{pmatrix}'; }], {useMathjax: true});
      
 </script> 
/*
This example is licensed under a 
Creative Commons Attribution ShareAlike 4.0 International License.
https://creativecommons.org/licenses/by-sa/4.0/

Please note you have to mention 
The Center of Mobile Learning with Digital Technology
in the credits.
*/

const BOARDID0 = 'your_div_id_0'; // Insert your 1st board id here!
const BOARDID1 = 'your_div_id_1'; // Insert your 2nd board id here!

  var board1 = JXG.JSXGraph.initBoard(BOARDID0, { boundingbox: [-7.5, 7.5, 12.5, -7.5], axis: true });
  var a = board1.create('slider', [[-5, -2], [5, -2], [-5, 1, 5]], { name: 'a', snapWidth: 0.1 });
  var b = board1.create('slider', [[-5, -3], [5, -3], [-5, 0, 5]], { name: 'b', snapWidth: 0.1 });
  var c = board1.create('slider', [[-5, -4], [5, -4], [-5, 0, 5]], { name: 'c', snapWidth: 0.1 });
  var d = board1.create('slider', [[-5, -5], [5, -5], [-5, 1, 5]], { name: 'd', snapWidth: 0.1 });

  var v = board1.create('point', [2, 2], { size: 3, name: 'v' });
  var w = board1.create('point', [-2, 1], { size: 3, name: 'w' });
  var va = board1.create('arrow', [[0, 0], v]);
  var wa = board1.create('arrow', [[0, 0], w]);

  var board2 = JXG.JSXGraph.initBoard(BOARDID1, { boundingbox: [-7.5, 7.5, 12.5, -7.5], axis: true });
  board1.addChild(board2);

  var v2 = board2.create('point', [
       () => a.Value() * v.X() + b.Value() * v.Y(),
       () => c.Value() * v.X() + d.Value() * v.Y()], 
       { face: '[]', size: 2, name: "v'" });
  var w2 = board2.create('point', [
       () => a.Value() * w.X() + b.Value() * w.Y(),
       () => c.Value() * w.X() + d.Value() * w.Y()], 
       { face: '[]', size: 2, name: "w'" });
  var va2 = board2.create('segment', [[0, 0], v2], { lastArrow: true });
  var wa2 = board2.create('segment', [[0, 0], w2], { lastArrow: true });
  
  board2.create('text', [-6, -2, () => '|' + (a.Value()).toFixed(2) + ' ' + (b.Value()).toFixed(2) +
          '|' + '<br>' + '|' + (c.Value()).toFixed(2) + ' ' + (d.Value()).toFixed(2) + '|']);

  // board2.create('text', [-6, 5, function() { return '\\begin{pmatrix}' + (a.Value()).toFixed(2) + ' &' + (b.Value()).toFixed(2) + '\\\\' +
  //        (c.Value()).toFixed(2) + '& ' + (d.Value()).toFixed(2) + '\\end{pmatrix}'; }], {useMathjax: true});
  
<jsxgraph width="75%, 75%" aspect-ratio="1 / 1, 1 / 1" numberOfBoards="2" title="Matrix multiplication" description="This construction was copied from JSXGraph examples database: BTW HERE SHOULD BE A GENERATED LINKuseGlobalJS="false">
   /*
   This example is licensed under a 
   Creative Commons Attribution ShareAlike 4.0 International License.
   https://creativecommons.org/licenses/by-sa/4.0/
   
   Please note you have to mention 
   The Center of Mobile Learning with Digital Technology
   in the credits.
   */
   
     var board1 = JXG.JSXGraph.initBoard(BOARDID0, { boundingbox: [-7.5, 7.5, 12.5, -7.5], axis: true });
     var a = board1.create('slider', [[-5, -2], [5, -2], [-5, 1, 5]], { name: 'a', snapWidth: 0.1 });
     var b = board1.create('slider', [[-5, -3], [5, -3], [-5, 0, 5]], { name: 'b', snapWidth: 0.1 });
     var c = board1.create('slider', [[-5, -4], [5, -4], [-5, 0, 5]], { name: 'c', snapWidth: 0.1 });
     var d = board1.create('slider', [[-5, -5], [5, -5], [-5, 1, 5]], { name: 'd', snapWidth: 0.1 });
   
     var v = board1.create('point', [2, 2], { size: 3, name: 'v' });
     var w = board1.create('point', [-2, 1], { size: 3, name: 'w' });
     var va = board1.create('arrow', [[0, 0], v]);
     var wa = board1.create('arrow', [[0, 0], w]);
   
     var board2 = JXG.JSXGraph.initBoard(BOARDID1, { boundingbox: [-7.5, 7.5, 12.5, -7.5], axis: true });
     board1.addChild(board2);
   
     var v2 = board2.create('point', [
          () => a.Value() * v.X() + b.Value() * v.Y(),
          () => c.Value() * v.X() + d.Value() * v.Y()], 
          { face: '[]', size: 2, name: "v'" });
     var w2 = board2.create('point', [
          () => a.Value() * w.X() + b.Value() * w.Y(),
          () => c.Value() * w.X() + d.Value() * w.Y()], 
          { face: '[]', size: 2, name: "w'" });
     var va2 = board2.create('segment', [[0, 0], v2], { lastArrow: true });
     var wa2 = board2.create('segment', [[0, 0], w2], { lastArrow: true });
     
     board2.create('text', [-6, -2, () => '|' + (a.Value()).toFixed(2) + ' ' + (b.Value()).toFixed(2) +
             '|' + '<br>' + '|' + (c.Value()).toFixed(2) + ' ' + (d.Value()).toFixed(2) + '|']);
   
     // board2.create('text', [-6, 5, function() { return '\\begin{pmatrix}' + (a.Value()).toFixed(2) + ' &' + (b.Value()).toFixed(2) + '\\\\' +
     //        (c.Value()).toFixed(2) + '& ' + (d.Value()).toFixed(2) + '\\end{pmatrix}'; }], {useMathjax: true});
     
</jsxgraph>

Matrix multiplication

Mappings
Vectors
On the first board, two vectors are shown. Sliders control the entries of a 2×2 transformation matrix. On the second board, the transformed vectors appear, updating in real time to visualize how the matrix manipulates their direction and scale.
Have also a look at the examples
Web references 
// Define the ids of your boards in BOARDID0, BOARDID1,...

  var board1 = JXG.JSXGraph.initBoard(BOARDID0, { boundingbox: [-7.5, 7.5, 12.5, -7.5], axis: true });
  var a = board1.create('slider', [[-5, -2], [5, -2], [-5, 1, 5]], { name: 'a', snapWidth: 0.1 });
  var b = board1.create('slider', [[-5, -3], [5, -3], [-5, 0, 5]], { name: 'b', snapWidth: 0.1 });
  var c = board1.create('slider', [[-5, -4], [5, -4], [-5, 0, 5]], { name: 'c', snapWidth: 0.1 });
  var d = board1.create('slider', [[-5, -5], [5, -5], [-5, 1, 5]], { name: 'd', snapWidth: 0.1 });

  var v = board1.create('point', [2, 2], { size: 3, name: 'v' });
  var w = board1.create('point', [-2, 1], { size: 3, name: 'w' });
  var va = board1.create('arrow', [[0, 0], v]);
  var wa = board1.create('arrow', [[0, 0], w]);

  var board2 = JXG.JSXGraph.initBoard(BOARDID1, { boundingbox: [-7.5, 7.5, 12.5, -7.5], axis: true });
  board1.addChild(board2);

  var v2 = board2.create('point', [
       () => a.Value() * v.X() + b.Value() * v.Y(),
       () => c.Value() * v.X() + d.Value() * v.Y()], 
       { face: '[]', size: 2, name: "v'" });
  var w2 = board2.create('point', [
       () => a.Value() * w.X() + b.Value() * w.Y(),
       () => c.Value() * w.X() + d.Value() * w.Y()], 
       { face: '[]', size: 2, name: "w'" });
  var va2 = board2.create('segment', [[0, 0], v2], { lastArrow: true });
  var wa2 = board2.create('segment', [[0, 0], w2], { lastArrow: true });
  
  board2.create('text', [-6, -2, () => '|' + (a.Value()).toFixed(2) + ' ' + (b.Value()).toFixed(2) +
          '|' + '<br>' + '|' + (c.Value()).toFixed(2) + ' ' + (d.Value()).toFixed(2) + '|']);

  // board2.create('text', [-6, 5, function() { return '\\begin{pmatrix}' + (a.Value()).toFixed(2) + ' &' + (b.Value()).toFixed(2) + '\\\\' +
  //        (c.Value()).toFixed(2) + '& ' + (d.Value()).toFixed(2) + '\\end{pmatrix}'; }], {useMathjax: true});

license

This example is licensed under a Creative Commons Attribution ShareAlike 4.0 International License.
Please note you have to mention The Center of Mobile Learning with Digital Technology in the credits.