Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 2 - Section 2.6 - Matrices - Exercises - Page 184: 5



Work Step by Step

We label the four elements of matrix $A$ using $a_{ij}$ to denote the element in the $(i,j)$th place. Then, we multiply using these elements as variables to obtain the system of equations: $2a_{11}+3a_{21}=3 2a_{12}+3a_{22}=0 a_{11}+4a_{21}=1 a_{12}+a_{22}=2$. Solving this in the familiar way gives $a_{11}=\frac{9}{5},a_{12}=6,a_{21}=\frac{−1}{5},a_{22}=−4.$
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