and Define \( T : \mathbb{R}^2 \to \mathbb{R}^2 \) by \( T(x) = A x \).
Find the image under \[ T \left( u = \begin{bmatrix} 1 \\ -3 \end{bmatrix}, \, v = \begin{bmatrix} u \\ u \end{bmatrix} \right) \]
b) Prove that a map \( T : \mathbb{R}^2 \to \mathbb{R}^2 \) defined by \( T(x,y) = (x,y) \) is linear.
\[ \begin{bmatrix} 1 & 6 & 2 & -5 \\ -1 & 0 & 3 & 1 \\ 0 & -1 & -2 & 3 \end{bmatrix} \]
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