Elementary Linear Algebra 7th Edition

Published by Cengage Learning
ISBN 10: 1-13311-087-8
ISBN 13: 978-1-13311-087-3

Chapter 2 - Matrices - 2.2 Properties of Matrix Operations - 2.2 Exercises - Page 60: 53

Answer

The second root of $B$ is $A=\left[\begin{array}{ccc}{3} &{0} \\{0}& {2} \end{array}\right]$.

Work Step by Step

Let the matrix $A$ be given by $$A=\left[\begin{array}{ccc}{3} &{0} \\{0}& {2} \end{array}\right].$$ Since $$A^2=\left[\begin{array}{ccc}{3} &{0} \\{0}& {2} \end{array}\right]\left[\begin{array}{ccc}{3} &{0} \\{0}& {2} \end{array}\right]=\left[\begin{array}{ccc}{9} &{0} \\{0}& {4} \end{array}\right]=B,$$ then the second root of $B$ is $A=\left[\begin{array}{ccc}{3} &{0} \\{0}& {2} \end{array}\right]$.
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