Linear Algebra and Its Applications (5th Edition)

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

Chapter 2 - Matrix Algebra - 2.2 Exercises - Page 111: 1

Answer

I will type matrices like this: (a b c/d e f), where (a b c) is the first row and (d e f) is the second row. (2 -3/$\frac{-5}{2}$ 4)

Work Step by Step

I will type matrices like this: (a b c/d e f), where (a b c) is the first row and (d e f) is the second row. This is a 2x2 matrix, therefore let A = (a b/ c d) if ad-bc $\ne$ 0. Thus, $A^{-1}$ = $\frac{1}{ad-bc}$ $\times$ (d -b/-c a) ad-bc = 8$\times$4 - 6$\times$5. Thus, ad-bc = 2 $A^{-1}$ = 1/2 $\times$ (4 -6/-5 8) which is (2 -3/$\frac{-5}{2}$ 4)
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