Elementary Linear Algebra 7th Edition

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

Chapter 3 - Determinants - Review Exercises - Page 139: 40

Answer

Since $\det(A)= 0$, then the system has no solutions or has infinite number of solutions.

Work Step by Step

Let $A$ be the coefficient matrix which is given by $$A=\left[ \begin {array}{ccc} 2&3&1\\ 2&-3&-3 \\ 8&6&0\end {array} \right] =\left[ \begin {array}{ccc} 2&3&1\\ 8&6&0 \\ 8&6&0\end {array} \right] .$$ One can calculate $\det(A)$ as follows $$\det(A)=(8)(6)-(6)(8)=0.$$ Since $\det(A)= 0$, then the system has no solutions or has infinite number of solutions.
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