Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 10 - Section 10.3 - Matrices and Systems of Linear Equations - 10.3 Exercises - Page 710: 31

Answer

$x=1$ $y=0$ $z=1$

Work Step by Step

$ \begin{bmatrix} 1 & 1 & 1 & 2\\ 2 & -3 & 2 & 4\\ 4 & 1 & -3 & 1 \end{bmatrix} $ Add -2 times the 1st row to the 2nd row to produce a new 2nd row. Add -4 times the 1st row to the 3rd row to produce a new 3rd row. $ \begin{bmatrix} 1 & 1 & 1 & 2\\ 0 & -5 & 0 & 0\\ 0 & -3 & -7 & -7 \end{bmatrix} $ From the second row we can express $-5y=0 \rightarrow y=0$ Use back-substitution to find the solution. $y=0$ $-3y-7z=-7 \rightarrow z=1$ $x+y+z=2 \rightarrow x=1$
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