Elementary Linear Algebra 7th Edition

Published by Cengage Learning
ISBN 10: 1-13311-087-8
ISBN 13: 978-1-13311-087-3

Chapter 2 - Matrices - 2.1 Operations with Matrices - 2.1 Exercises - Page 50: 71


It gives an inconsistent system of equations.

Work Step by Step

Assume that the matrix $A$ is given by $$A=\left[\begin{array}{cc}{x_1} &{x_2} \\{x_3}& {x_4} \end{array}\right],$$ then we have the system $$ \begin{aligned} x_{1}+x_{3}&=1 \\ x_{2} +x_4 &=0\\ x_1+x_{3} &=0\\ x_{2} +x_4 &=1 \end{aligned}. $$ It easy to see that the above system is not consistent since it gives $0=1$ which is a contradiction.
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