College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 5 - Section 5.2 - Matrix Solution of Linear Systems - 5.2 Exercises - Page 499: 8

Answer

\[ \left[ \begin{array}{ccc|c} 4 & -2 & 3 &4 \\ 3 & 5 & 1 &7\\5&-1&4&7 \end{array} \right] \]

Work Step by Step

We will write the given equations in such a form that the variables terms are on the left-hand side and the constants on the right-hand side. Thus, we have: $4x-2y+3z=4 \quad\quad \text{(Add 4 to both sides of the first equation.)}\\ 3x+5y+z=7 \quad\quad \text{(Add 7 from both sides of the first equation.)}\\5x-y+4z=7 \quad\quad \text{(Add 7 to both sides of the third equation.)}$ We transform the above equations into a $3 \times 4$ matrix such that the coefficients of the variables are on the left-hand side and the constants on the right-hand side of the vertical bar. Therefore, the $3 \times 4$ matrix can be expressed as: \[ \left[ \begin{array}{ccc|c} 4 & -2 & 3 &4 \\ 3 & 5 & 1 &7\\5&-1&4&7 \end{array} \right] \]
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