Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 8 - Systems of Linear Equations and Problem Solving - 8.7 Determinants and Cramer's Rule - 8.7 Exercise Set - Page 557: 16



Work Step by Step

We use Cramer's rule to find the determinant of the matrix. Doing this, we obtain: $$ \det \begin{pmatrix}2&-1&1\\ 1&2&-1\\ 3&4&-3\end{pmatrix}\\ 2\cdot \det \begin{pmatrix}2&-1\\ 4&-3\end{pmatrix}-\left(-1\right)\det \begin{pmatrix}1&-1\\ 3&-3\end{pmatrix}+1\cdot \det \begin{pmatrix}1&2\\ 3&4\end{pmatrix}\\ 2\left(-2\right)-\left(-1\right)\cdot \:0+1\cdot \left(-2\right)\\ -6$$
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