1. Let $T: M_{2x2} \rightarrow P_2$ be a linear transformation such that
$T \begin{pmatrix} 1 & 0 \ 0 & 0 \end{pmatrix} = 1 - x$
$T \begin{pmatrix} 1 & 1 \ 0 & 0 \end{pmatrix} = 1 + x + x^2$
$T \begin{pmatrix} 1 & 1 \ 1 & 0 \end{pmatrix} = 2x - x^2$
$T \begin{pmatrix} 1 & 1 \ 1 & 0 \end{pmatrix} = 2 + x - 2x^2$
Find
(a) $T \begin{pmatrix} a & b \ c & d \end{pmatrix}$
(b) $T \begin{pmatrix} a & 2a \ 3a & 4a \end{pmatrix}$
2. Let $T: R^3 \rightarrow R^2$ be a linear transformation such that
$T(1,2,1) = (1,0)$
$T(2,9,0) = (-1,1)$
$T(3,3,4) = (0,1)$
Find
(a) T(x, y, z)
(b) T(x, 2x, 3x)
