a. The linear transformation $T_1: \mathbb{R}^2 \to \mathbb{R}^2$ is given by:
$T_1(x, y) = (2x + 9y, 8x + 37y)$.
Find $T_1^{-1}(x, y)$.
$T_1^{-1}(x, y) = (\frac{37}{2}x + \frac{-9}{2}y, -4x + y)$
b. The linear transformation $T_2: \mathbb{R}^3 \to \mathbb{R}^3$ is given by:
$T_2(x, y, z) = (x + 2z, 2x + y, 2y + z)$.
Find $T_2^{-1}(x, y, z)$.
$T_2^{-1}(x, y, z) = (\frac{1}{2}x + \frac{1}{2}y + \frac{-1}{2}z, \frac{-1}{2}x + \frac{1}{2}y + \frac{1}{2}z, \frac{1}{2}x + \frac{-1}{2}y + \frac{1}{2}z)$
