Chapter 10 - 10.2 - Operations with Matrices - 10.2 Exercises - Page 726: 71

Part A: $\begin{bmatrix} 1 & -5 & 2\\ -3 & 1 & -1\\ 0 & -2 & 5\\ \end{bmatrix}$$\begin{bmatrix} x_{1}\\ x_{2}\\ x_{3}\\ \end{bmatrix}$ = $\begin{bmatrix} -20\\ 8\\ -16\\ \end{bmatrix}$ Part B: $\begin{bmatrix} x_{1}\\ x_{2}\\ x_{3}\\ \end{bmatrix}$ = $\begin{bmatrix} -1\\ 3\\ -2\\ \end{bmatrix}$

Part A: $\begin{bmatrix} 1 & -5 & 2\\ -3 & 1 & -1\\ 0 & -2 & 5\\ \end{bmatrix}$$\begin{bmatrix} x_{1}\\ x_{2}\\ x_{3}\\ \end{bmatrix}$ = $\begin{bmatrix} -20\\ 8\\ -16\\ \end{bmatrix}$ Part B: Gauss Jordan Elimination: $\begin{bmatrix} 1 & -5 & 2 & |-20\\ -3 & 1 & -1 & |8\\ 0 & -2 & 5 & |-16\\ \end{bmatrix}$ ~ $\begin{bmatrix} 1 & -5 & 2 & |-20\\ 0 & 14 & -5 & |52\\ 0 & -2 & 5 & |-16\\ \end{bmatrix}$ ~ $\begin{bmatrix} 1 & -5 & 2 & |-20\\ 0 & 14 & -5 & |52\\ 0 & 0 & 30 & |-60\\ \end{bmatrix}$ ~ $\begin{bmatrix} 1 & -5 & 0 & |-16\\ 0 & 14 & 0 & |42\\ 0 & 0 & 1 & |-2\\ \end{bmatrix}$ ~ $\begin{bmatrix} 1 & -5 & 0 & |-16\\ 0 & 1 & 0 & |3\\ 0 & 0 & 1 & |-2\\ \end{bmatrix}$ ~ $\begin{bmatrix} 1 & 0 & 0 & |-1\\ 0 & 1 & 0 & |3\\ 0 & 0 & 1 & |-2\\ \end{bmatrix}$ Therefore the answer is: $\begin{bmatrix} x_{1}\\ x_{2}\\ x_{3}\\ \end{bmatrix}$ = $\begin{bmatrix} -1\\ 3\\ -2\\ \end{bmatrix}$