Elementary Linear Algebra 7th Edition

Published by Cengage Learning
ISBN 10: 1-13311-087-8
ISBN 13: 978-1-13311-087-3

Chapter 1 - Systems of Linear Equations - Review Exercises: 33

Answer

$x=3t+4$ $y=2t+5$ $z=t$

Work Step by Step

Write the augmented matrix of the system of linear equations. $ \begin{bmatrix} 1 & -2 & 1& -6\\ 2 & -3 & 0 & -7\\ -1 & 3& -3 & 11 \end{bmatrix} $ Add -2 times the 1st row to the 2nd row to produce a new 2nd row. Add 1 times the 1st row to the 3rd row to produce a new 3rd row. $ \begin{bmatrix} 1 & -2 & 1& -6\\ 0 & 1 & -2 & 5\\ 0 & 1& -2 & 5 \end{bmatrix} $ Add -1 times the 2nd row to the 3rd row to produce a new 3rd row. $ \begin{bmatrix} 1 & -2 & 1& -6\\ 0 & 1 & -2 & 5\\ 0 & 0&0 & 0 \end{bmatrix} $ Use the parameter t to represent z(where t is any real number) and substitute further for x and y. $z=t$ $y=2t+5$ $x=3t+4$
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