define a transformation T:mathbbR3 to mathbbR2 by T(x) = Ax where a. Find T(u) b. Find x in mathbbR3 whose image under T is b c. Is x unique?

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

$$A = \begin{bmatrix} 1 & -5 & -7 \ -3 & 7 & 5 \end{bmatrix}, \quad u = \begin{bmatrix} 1 \ 2 \ 3 \end{bmatrix}, \quad b = \begin{bmatrix} -2 \ -2 \end{bmatrix}, \quad T(x) = Ax$$

a. Find $T(u)$

b. Find $x \in \mathbb{R}^3$ whose image under $T$ is $b$

c. Is $x$ unique?

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