a. The linear transformation $T_1: R^2 \rightarrow R^2$ is given by:

$T_1(x, y) = (2 x + 5 y, 8 x + 21 y)$.

Find $T_1^{-1}(x, y)$.

$T_1^{-1}(x, y) = ($x + y, x + y$)$


b. The linear transformation $T_2: R^3 \rightarrow R^3$ is given by:

$T_2(x, y, z) = (x + 1 z, 2 x + y, 2 y + z)$.

Find $T_2^{-1}(x, y, z)$.

$T_2^{-1}(x, y, z) = ($x + y + z, x + y + z, x + y + z$)$


c. Using $T_1$ from part a, it is given that:

$T_1(x, y) = (3, -4)$

Find x and y.

$x =$ $y =$


d. Using $T_2$ from part b, it is given that:

$T_2(x, y, z) = (5, -5, 1)$

Find x, y, and z.

$x =$ $y =$ $z =$