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  • First define the form you want. You could later deploy this form to the wolfram cloud with CloudDeploy so users could change the inputs on a webpage. Otherwise they can download the code to the desktop and input their own changes to the boxes in the form and click okay.
    • In[]:=
    tranmatplot=FormPage[{{"a","Enter a 2x2 matrix as a list {} with each row as a sublist {} separated by a comma , (e.g. {{1,2},{2,1}}) :"}"String",{"x","Enter a 2x1 vector x as a list {x,y} separated by a comma , (e.g. {1,2}) :"}"String",{"color2","Select Original vector x plot color:"}{Red,Green,Blue,Purple,Pink,Orange,Black},{"color","Select transformed vector b color after being Multiplied by Matrix A:"}{Red,Green,Blue,Purple,Pink,Orange,Black}},Show[Rasterize[Row[{Framed[Labeled[MatrixForm[a=Function[t,ToExpression[#a]][t]]," Matrix A ",Top]],Framed[Labeled[MatrixForm[x=Function[t,ToExpression[#x]][t]]," Vector x ",Top]],Framed[Labeled[Det[a],"Determinant of A",Top]],Framed[Labeled[MatrixForm[b=a.x]," Vector b ",Top]],​​Show[Graphics[{{#color2,Thick,Arrow[{{0,0},x}]},{#color,Thickness[Medium],Arrow[{{0,0},b}]}},AxesTrue,GridLinesAutomatic,PlotLabel"Vector x becomes b after Transformation by Matrix A"],ImageSizeLarge]}],ImageResolution450],ImageSizeLarge]&,PageTheme"Red"]
    Out[]=
    Enter a 2x2 matrix as a list {} with each row as a sublist {} separated by a comma , (e.g. {{1,2},{2,1}}) :
    {{1,2},{2,1}}
    Enter a 2x1 vector x as a list {x,y} separated by a comma , (e.g. {1,2}) :
    {3,4}
    Select Original vector x plot color:
    Select transformed vector b color after being Multiplied by Matrix A:
    OK