Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 11 - Systems of Equations and Inequalities - 11.2 Systems of Linear Equations: Matrices - 11.2 Assess Your Understanding - Page 731: 30


Inconsistent No solution

Work Step by Step

We are given the reduced row echelon form of a system of linear equations: $\begin{bmatrix}1&0&0&|&0\\0&1&0&|&0\\0&0&0&|&2\end{bmatrix}$ Write the system of equations corresponding to the given matrix: $\begin{cases} 1x+0y+0z=0\\ 0x+1y+0z=0\\ 0x+0y+0z=2 \end{cases}$ $\begin{cases} x=0\\ y=0\\ 0=2 \end{cases}$ Because the reduced row echelon form has a row with only zeros at the left of the bar and a nonzero element at the right of the bar, the system is inconsistent, and it has no solution.
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