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 - 11.3 Systems of Linear Equations: Determinants - 11.3 Assess Your Understanding - Page 742: 48

Answer

$4$.

Work Step by Step

We know that for determinants: (i) if two rows/columns were interchanged, the value of the original determinant gets multiplied by $-1$ (ii) if any row/column was multiplied by a constant $k$, the value of the original determinant gets multiplied by $k$ (iii) if any row/column was multiplied by a constant $k$ ($k\ne0$), and then this is added to another row/column, the value of the original determinant remains unchanged Hence here because $-1$ times column $1$ is added to column $3$, according to Rule (iii) the value of the determinant is $4$.
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