Chapter 10 - 10.2 - Operations with Matrices - 10.2 Exercises - Page 724: 9

Part A: $\begin{bmatrix} 3 & -2\\ 1 & 7\\ \end{bmatrix}$ Part B: $\begin{bmatrix} -1 & 0\\ 3 & -9\\ \end{bmatrix}$ Part C: $\begin{bmatrix} 3 & -3\\ 6 & -3\\ \end{bmatrix}$ Part D: $\begin{bmatrix} -1 & -1\\ 8 & -19\\ \end{bmatrix}$

Part A: $\begin{bmatrix} 1+2 & -1-1\\ 2-1 & -1+8\\ \end{bmatrix}$ = $\begin{bmatrix} 3 & -2\\ 1 & 7\\ \end{bmatrix}$ Part B: $\begin{bmatrix} 1-2 & -1+1\\ 2+1 & -1-8\\ \end{bmatrix}$ = $\begin{bmatrix} -1 & 0\\ 3 & -9\\ \end{bmatrix}$ Part C: $\begin{bmatrix} 3(1) & 3(-1)\\ 3(2) & 3(-1)\\ \end{bmatrix}$ = $\begin{bmatrix} 3 & -3\\ 6 & -3\\ \end{bmatrix}$ Part D: First, find 2B: $\begin{bmatrix} 2(2) & 2(-1)\\ 2(-1) & 2(8)\\ \end{bmatrix}$ = $\begin{bmatrix} 4 & -2\\ -2 & 16\\ \end{bmatrix}$ Then, find 3A - 2B: $\begin{bmatrix} 3-4 & -3+2\\ 6+2 & -3-16\\ \end{bmatrix}$ = $\begin{bmatrix} -1 & -1\\ 8 & -19\\ \end{bmatrix}$