Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 10 - 10.1 - Matrices and Systems of Equations - 10.1 Exercises - Page 711: 77

Answer

x = 7 y = -3 z = 4

Work Step by Step

NOTE: Gauss-Jordan elimination will reduce until the matrix is in reduced row-echelon form. $\begin{bmatrix} -1 & 1 & -1 & |-14\\ 2 & -1 & 1 & |21\\ 3 & 2 & 1 & |19\\ \end{bmatrix}$ ~ $\begin{bmatrix} -1 & 1 & -1 & |-14\\ 0 & 1 & -1 & |-7\\ 0 & 5 & -2 & |-23\\ \end{bmatrix}$ ~ $\begin{bmatrix} -1 & 1 & -1 & |-14\\ 0 & 1 & -1 & |-7\\ 0 & 0 & 3 & |12\\ \end{bmatrix}$ ~ $\begin{bmatrix} -1 & 1 & -1 & |-14\\ 0 & 1 & -1 & |-7\\ 0 & 0 & 1 & |4\\ \end{bmatrix}$ ~ $\begin{bmatrix} -1 & 1 & 0 & |-10\\ 0 & 1 & 0 & |-3\\ 0 & 0 & 1 & |4\\ \end{bmatrix}$ ~ $\begin{bmatrix} 1 & -1 & 0 & |10\\ 0 & 1 & 0 & |-3\\ 0 & 0 & 1 & |4\\ \end{bmatrix}$ ~ $\begin{bmatrix} 1 & 0 & 0 & |7\\ 0 & 1 & 0 & |-3\\ 0 & 0 & 1 & |4\\ \end{bmatrix}$ From reduced row-echelon form the solution is simple: x = 7 y = -3 z = 4
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