College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 8 - Section 8.4 - Matrix Algebra - 8.4 Assess Your Understanding - Page 599: 73

Answer

$x\approx-1.19, \ y\approx 2.46, \ z\approx 8.27$ or $(-1.19, \ 2.46, \ 8.27 )$

Work Step by Step

Writing the system in matrix form, $AX=B,$ the solution is $X=A^{-1}B$. Here, $A=\left[\begin{array}{rrr}{25}&{61}&{-12}\\{18}&{-2}&{4}\\{8}&{35}&{21}\end{array}\right], \quad B=\left[\begin{array}{l} 21\\ 7\\ -2 \end{array}\right]$ Using desmos.com/matrix here: Select "New matrix", define the dimensions (3 by 3), and enter the matrix entries for A. Do the same for the (3 by 1) matrix B.... Enter $A^{-1}B$ (see screenshot) we find $X\approx\left[\begin{array}{l} -1.19\\ 2.46\\ 8.27 \end{array}\right]$ $x\approx-1.19, \ y\approx 2.46, \ z\approx 8.27$ or $(-1.19, \ 2.46, \ 8.27 )$
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