Finite Math and Applied Calculus (6th Edition)

Published by Brooks Cole
ISBN 10: 1133607705
ISBN 13: 978-1-13360-770-0

Chapter 3 - Section 3.2 - Using Matrices to Solve Systems of Equations - Exercises - Page 203: 3

Answer

$(6,6)$

Work Step by Step

Write the augmented matrix and, using row transformations arrive at the reduced row echelon form (rref). Properties of rref: P1. Leading entry of each row is a 1. P2. The columns of the leading entries are clear P3. The leading entry in each row is to the right of the leading entry in the row above, and any rows of zeros are at the bottom. ----------- $\left[\begin{array}{lll} 3 & -2 & 6\\ 2 & -3 & -6 \end{array}\right]\left[\begin{array}{l} .\\ 3R_{2}-2R_{1} \end{array}\right.$, clear column 1 $\left[\begin{array}{lll} 3 & -2 & 6\\ 0 & -5 & -30 \end{array}\right]\left[\begin{array}{l} .\\ -\frac{1}{5}R_{2} \end{array}\right.$, leading 1 in row 2 $\left[\begin{array}{lll} 3 & -2 & 6\\ 0 & 1 & 6 \end{array}\right]\left[\begin{array}{l} R_{1}+2R_{2}.\\ . \end{array}\right.$, clear column 2 $\rightarrow\left[\begin{array}{lll} 3 & 0 & 18\\ 0 & 1 & 6 \end{array}\right]\left[\begin{array}{l} \frac{1}{6}R_{1}.\\ . \end{array}\right.$, leading 1 in row 1 $\left[\begin{array}{lll} 1 & 0 & 6\\ 0 & 1 & 6 \end{array}\right]$ Interpret as equations: $x=6$ $y=6$ Solution: $(6,6)$
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