Linear Algebra and Its Applications (5th Edition)

Published by Pearson
ISBN 10: 032198238X
ISBN 13: 978-0-32198-238-4

Chapter 2 - Matrix Algebra - Supplementary Exercises - Page 163: 18

Answer

See explanation

Work Step by Step

By hypothesis, $A$ is $5 \times 3, C$ is $3 \times 5,$ and $A C=I 3 .$ let $\mathrm{x}$ satisfies $\mathrm{Ax}=\mathrm{b} .$ Then $\mathrm{CAx}=\mathrm{Cb} .$ because $\mathrm{CA}=\mathrm{I}, \mathrm{x}$ must be Cb. This shows that Cb is the only solution of $\mathrm{Ax}=b$
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