13. Let $T_1: P_1 \to P_2$ be the linear transformation defined by
$T_1(c_0 + c_1x) = 2c_0 - 3c_1x$
and let $T_2: P_2 \to P_3$ be the linear transformation defined by
$T_2(c_0 + c_1x + c_2x^2) = 3c_0x + 3c_1x^2 + 3c_2x^3$
Let $B = \{1, x\}$, $B'' = \{1, x, x^2\}$, and $B' = \{1, x, x^2, x^3\}$.
a. Find $[T_2 \circ T_1]_{B', B}$, $[T_2]_{B', B''}$, and $[T_1]_{B'', B}$.
b. State a formula relating the matrices in part (a).
c. Verify that the matrices in part (a) satisfy the formula you
stated in part (b).