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: 34

Answer

$(3,1,2)$

Work Step by Step

Write the augmented matrix and, using row transformations, arrive at the row-reduced echelon form. $\left[\begin{array}{llll} 0 & 2 & 1 & 4\\ 1 & 1 & 0 & 4\\ 3 & 3 & -1 & 10 \end{array}\right]$ Swap rows 1 and 2, $\left[\begin{array}{llll} 1 & 1 & 0 & 4\\ 0 & 2 & 1 & 4\\ 3 & 3 & -1 & 10 \end{array}\right] \ \ \begin{array}{l} .\\ .\\ R_{3}-3R_{1}\rightarrow R_{3}. \end{array}$ $\left[\begin{array}{llll} 1 & 1 & 0 & 4\\ 0 & 2 & 1 & 4\\ 0 & 0 & -1 & -2 \end{array}\right] \ \ \begin{array}{l} .\\ +R_{3}.\\ \times(-1). \end{array}$ $\left[\begin{array}{llll} 1 & 1 & 0 & 4\\ 0 & 2 & 0 & 2\\ 0 & 0 & 1 & 2 \end{array}\right]\ \ \begin{array}{l} .\\ \div 2.\\ . \end{array}$ $\left[\begin{array}{llll} 1 & 1 & 0 & 4\\ 0 & 1 & 0 & 1\\ 0 & 0 & 1 & 2 \end{array}\right]\ \ \begin{array}{l} -R_{2}.\\ .\\ . \end{array}$ $\left[\begin{array}{llll} 1 & 0 & 0 & 3\\ 0 & 1 & 0 & 1\\ 0 & 0 & 1 & 2 \end{array}\right]$ Solution: $(3,1,2)$
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