Find the standard matrix for the linear transformation defined by the equations ω1 = 2x1-3x2+x4 and ω2 = 3x1+5x2-x3.

Question

Find the standard matrix for the linear transformation defined by the equations [latex]{\omega }_{1}=2x_{1}-3x_{2}+x_{4}[/latex] and [latex]{\omega }_{2}=3x_{1}-5x_{2}+x_{3}[/latex] .

Accepted Answer

Let linear transformation of the above equation be denoted by $T\colon R^{4}\to R^{2},$ $T\bigl(x_{1},x_{2},x_{3},x_{4}\bigr)=\bigl(w_{1},w_{2}\bigr)=\bigl(2x_{1}-3x_{2}+x_{4},3x_{1}+5x_{2}-x_{3}\bigr)$

Therefore, the standard matrix T is

T=\left[\begin{array}{c c c c}{{\ 2}}&{{-3}}&{{\ \ \ 0}}&{{1}}\\ {{\ 3}}&{{\ \ \ 5}}&{{-1}}&{{0}}\end{array}\right].

Therefore, the standard matrix T is

[latex]T=\left[\begin{array}{c c c c}{{\ 2}}&{{-3}}&{{\ \ \ 0}}&{{1}}\ {{\ 3}}&{{\ \ \ 5}}&{{-1}}&{{0}}\end{array} ight].[/latex]

Question 1.3: Find the standard matrix for the linear transformation defin......

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