Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 10 - Section 10.6 - Determinants and Cramer's Rule - 10.6 Exercises - Page 743: 23

Answer

5000, Yes.

Work Step by Step

Evaluate the determinant with cofactors: $\begin{array}( \\|A|= \\ \\ \end{array} \begin{vmatrix} 30 & 0 &20\\0 &-10 &-20\\40 &0 &10\end{vmatrix} \begin{array}( \\=30 \\ \\\end{array}\begin{vmatrix} -10 &-20\\0 &10 \end{vmatrix} \begin{array}( \\+20 \\ \\\end{array} \begin{vmatrix} 0 &-10\\40 &0 \end{vmatrix}$ $|A|=30(-100)+20(400)=5000$ As $|A|\ne0$, the matrix should have an inverse.
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