Define linear transformation with an example. Let and define a transformation T: mathbbR2 to mathbbR3 by T(x) = Ax then a. find T(v) b. find x in mathbbR2 whose image under T is b

Define linear transformation with an example. Let $$A = \begin{bmatrix} 1 & -3 \ 3 & 5 \ -1 & 7 \end{bmatrix}, \quad v = \begin{bmatrix} 2 \ -1 \end{bmatrix}, \quad b = \begin{bmatrix} 3 \ 2 \ 4 \end{bmatrix}, \quad x = \begin{bmatrix} x_1 \ x_2 \end{bmatrix}$$

and define a transformation $T: \mathbb{R}^2 \to \mathbb{R}^3$ by $T(x) = Ax$ then

a. find $T(v)$

b. find $x \in \mathbb{R}^2$ whose image under $T$ is $b$ [10]