Chapter 10 - 10.2 - Operations with Matrices - 10.2 Exercises - Page 725: 46

Part A: $\begin{bmatrix} -6 & 12\\ -4 & -16\\ \end{bmatrix}$ Part B: $\begin{bmatrix} -12 & -6\\ 4 & -10\\ \end{bmatrix}$ Part C: $\begin{bmatrix} 30 & 6\\ -4 & 10\\ \end{bmatrix}$

Part A: $\begin{bmatrix} 6(-2) + 3(2) & 6(0) + 3(4)\\ -2(-2) + (-4)(2) & (-2)(0) + (-4)(4)\\ \end{bmatrix}$ = $\begin{bmatrix} -12+6 & 0+12\\ 4-8 & 0-16\\ \end{bmatrix}$ = $\begin{bmatrix} -6 & 12\\ -4 & -16\\ \end{bmatrix}$ Part B: $\begin{bmatrix} -2(6) + 0(-2) & -2(3) + 0(-4)\\ 2(6) + 4(-2) & 2(3) + 4(-4)\\ \end{bmatrix}$ = $\begin{bmatrix} -12+0 & -6+0\\ 12-8 & 6-16\\ \end{bmatrix}$ = $\begin{bmatrix} -12 & -6\\ 4 & -10\\ \end{bmatrix}$ Part C: $\begin{bmatrix} 6(6) + 3(-2) & 6(3) + 3(-4)\\ -2(6) + (-4)(-2) & (-2)(3) + (-4)(-4)\\ \end{bmatrix}$ = $\begin{bmatrix} 36-6 & 18-12\\ -12+8 & -6+16\\ \end{bmatrix}$ = $\begin{bmatrix} 30 & 6\\ -4 & 10\\ \end{bmatrix}$