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Determine whether the function [tex]F[/tex] is a linear transformation.
(i) [tex]F: \mathbb{R}^2 \rightarrow \mathbb{R}^3[/tex] defined by [tex]F\left(\left[\begin{array}{c}x_1 \\ x_2\end{array}\right]\right)=\left[\begin{array}{c}x_1-x_2 \\ -x_1+x_2 \\ x_2\end{array}\right][/tex]
(ii) [tex]F: \mathbb{R}^2 \rightarrow \mathbb{R}[/tex] defined by [tex]F\left(\left[\begin{array}{c}x_1 \\ x_2\end{array}\right]\right)=\left|x_1\right|+\left|x_2\right|[/tex]
Sagot :
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