Chapter 10 - 10.2 - Operations with Matrices - 10.2 Exercises - Page 725: 47

Part A: $\begin{bmatrix} 5 & -9 & 0\\ 3 & 0 & -8\\ -1 & 4 & 11\\ \end{bmatrix}$ Part B: $\begin{bmatrix} 5 & -9 & 0\\ 3 & 0 & -8\\ -1 & 4 & 11\\ \end{bmatrix}$ Part C: $\begin{bmatrix} -2 & -45 & 72\\ 23 & -59 & -88\\ -4 & 53 & 89\\ \end{bmatrix}$

Part A: $\begin{bmatrix} 5(1) + (-9)(0) + 0(0) & 5(0) + (-9)(1) + 0(0) & 5(0) + (-9)(0) + 0(1)\\ 3(1) + 0(0) + (-8)(0) & 3(0) + 0(1) + (-8)(0) & 3(0) + 0(0) + (-8)(1)\\ (-1)(1) + 4(0) + 11(0) & (-1)(0) + 4(1) + 11(0) & (-1)(0) + 4(0) + 11(1)\\ \end{bmatrix}$ = $\begin{bmatrix} 5+0+0 & 0-9+0 & 0+0+0\\ 3+0+0 & 0+0+0 & 0+0-8\\ -1+0+0 & 0+4+0 & 0+0+11\\ \end{bmatrix}$ = $\begin{bmatrix} 5 & -9 & 0\\ 3 & 0 & -8\\ -1 & 4 & 11\\ \end{bmatrix}$ Part B: $\begin{bmatrix} 1(5) + 0(3) + 0(-1) & 1(-9) + 0(0) + 0(4) & 1(0) + 0(-8) + 0(11)\\ 0(5) + 1(3) + 0(-1) & 0(-9) + 1(0) + 0(4) & 0(0) + 1(-8) + 0(11)\\ 0(5) + 0(3) + 1(-1) & 0(-9) + 0(0) + 1(4) & 0(0) + 0(-8) + 1(11)\\ \end{bmatrix}$ = $\begin{bmatrix} 5+0+0 & -9+0+0 & 0+0+0\\ 0+3+0 & 0+0+0 & 0-8+0\\ 0+0-1 & 0+0+4 & 0+0+11\\ \end{bmatrix}$ = $\begin{bmatrix} 5 & -9 & 0\\ 3 & 0 & -8\\ -1 & 4 & 11\\ \end{bmatrix}$ Part C: $\begin{bmatrix} 5(5) + (-9)(3) + 0(-1) & 5(-9) + (-9)(0) + 0(4) & 5(0) + (-9)(-8) + 0(11)\\ 3(5) + 0(3) + (-8)(-1) & 3(-9) + 0(0) + (-8)(4) & 3(0) + 0(-8) + (-8)(11)\\ (-1)(5) + 4(3) + 11(-1) & (-1)(-9) + 4(0) + 11(4) & (-1)(0) + 4(-8) + 11(11)\\ \end{bmatrix}$ = $\begin{bmatrix} 25-27+0 & -45+0+0 & 0+72+0\\ 15+0+8 & -27+0-32 & 0+0-88\\ -5+12-11 & 9+0+44 & 0-32+121\\ \end{bmatrix}$ = $\begin{bmatrix} -2 & -45 & 72\\ 23 & -59 & -88\\ -4 & 53 & 89\\ \end{bmatrix}$