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: 10

Answer

a) $AB$ is defined with size 3x5 b) $BA$ is not defined c) $AC$ is defined with size 3x4 d) $CA$ is not defined e) $BC$ is not defined f) $CB$ is defined with size 4x5

Work Step by Step

If $U, V$ are matrices of sizes $u_r \times u_c$ and $v_r \times v_c$ respectively, $UV$ is defined if and only if $u_c=v_r$. The size of $UV$ is $u_r\times v_c$. So for $A, B, C$ with sizes 3x4, 4x5, and 4x4 respectively, a) $AB$ is defined with size 3x5. b) $BA$ is not defined. c) $AC$ is defined with size 3x4. d) $CA$ is not defined. e) $BC$ is not defined. f) $CB$ is defined with size 4x5.
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