Perform the indicated matrix operations given that A, B and C are defined as follows. If an operation is not defined, state the reason.

A - C

In Exercises 37 - 44, perform the indicated matrix operations given that A, B and C are defined as follows. If an operation is not defined, state the reason.

A(BC)

Solve the system: (Hint: Let A = ln w, B = ln x, C = ln y, and D = ln z. Solve the system for A, B, C, and D. Then use the logarithmic equations to find w, x, y, and z.)

$\(\begin{cases}\) 2 \(\ln\) w + \(\ln\) x + 3 \(\ln\) y - 2 \(\ln\) z = -6 \\ 4 \(\ln\) w + 3 \(\ln\) x + \(\ln\) y - \(\ln\) z = -2 \\ \(\ln\) w + \(\ln\) x + \(\ln\) y + \(\ln\) z = -5 \\ \(\ln\) w + \(\ln\) x - \(\ln\) y - \(\ln\) z = 5 \(\end{cases}\)$

In Exercises 39–42, find A^(-1) Check that AA^-1 = I and A^(-1)A = I

Find the cubic function f(x) = ax³ + bx² + cx + d for which ƒ( − 1) = 0, ƒ(1) = 2, ƒ(2) = 3, and ƒ(3) = 12.

In Exercises 37–44, use Cramer's Rule to solve each system. $\(\begin{cases}\) x + y + z = 4 \\ x - 2y + z = 7 \\ x + 3y + 2z = 4 \(\end{cases}\)$

a. Write each linear system as a matrix equation in the form AX = B. b. Solve the system using the inverse that is given for the coefficient matrix.

$\(\begin{cases}\) w - x + 2y \(\quad\)\(\quad\) = -3 \\ \(\quad\[\quad\) x - y + z = 4 \\ -w + x - y + 2z = 2 \\ \(\quad\]\quad\) -x + y - 2z = -4 \(\end{cases}\) \\ \(\text{The inverse of }\) \(\begin{bmatrix}\) 1 & -1 & 2 & 0 \\ 0 & 1 & -1 & 1 \\ -1 & 1 & -1 & 2 \\ 0 & -1 & 1 & -2 \(\end{bmatrix}\) \(\text{ is }\) \(\begin{bmatrix}\) 0 & 0 & -1 & -1 \\ 1 & 4 & 1 & 3 \\ 1 & 2 & 1 & 2 \\ 0 & -1 & 0 & -1 \(\end{bmatrix}\)$