Find the standard matrix for the linear transformation T defined by the formula T(x1,x2) = (x2,-x1,x1+3x2,x1-x2) .

Question

Find the standard matrix for the linear transformation T defined by the formula [latex]T\bigl(x_{1},x_{2}\bigr)=\bigl(x_{2},-\,x_{1},x_{1}+3x_{2},\,x_{1}-x_{2}\bigr).[/latex]

Accepted Answer

The standard matrix for the linear transformation [latex]T\bigl(x_{1},x_{2}\bigr)=\bigl(x_{2},-x_{1},x_{1}+3x_{2},x_{1}-x_{2}\bigr)[/latex] is

[latex]T=\left[\begin{array}{c c c}{{\ \ 0}}&{{\ \ 1}}\ {{-1}}&{{\ \ 0}}\ {\ \ \ {1}}&{{\ \ 3}}\ {{\ \ \ 1}}&{{-1\ }}\end{array} ight].[/latex]

Question 1.4: Find the standard matrix for the linear transformation T def......

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