Define linear transformation with an example.

Let A = \(\begin{bmatrix}1 & -3\\ 3 & 5\\ -1 & 7\end{bmatrix}\), v = \(\begin{bmatrix}2\\ -1\end{bmatrix}\), b = \(\begin{bmatrix}3\\ 2\\ 4\end{bmatrix}\), x = \(\begin{bmatrix}x_1\\ x_2\end{bmatrix}\)

and define a transformation T:R² → R² by T(x) = Ax then

1. find T(v)
2. find x ∈ R² whose image under T is b