23. Let a A = [3 2]. B=[ª b]. d and ¹= [1 2]. Find B so that AB = I= BA as follows: First equate en- tries on the two sides of the equation AB = I. Then solve the resulting four equations for a, b, c, and d. Finally verify that BA = I as well.

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter9: Systems Of Linear Equations
Section9.7: Puzzle Problems
Problem 8OE
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Question
Problems 23 through 26 introduce the idea-developed more
fully in the next section of a multiplicative inverse of a square
matrix.
23. Let
2
А
B =
=
A-[39]- *-[23]
2]. = [a b].
¹ = [1 2].
and
Find B so that AB = I= BA as follows: First equate en-
tries on the two sides of the equation AB = I. Then solve
the resulting four equations for a, b, c, and d. Finally
verify that BA = I as well.
Transcribed Image Text:Problems 23 through 26 introduce the idea-developed more fully in the next section of a multiplicative inverse of a square matrix. 23. Let 2 А B = = A-[39]- *-[23] 2]. = [a b]. ¹ = [1 2]. and Find B so that AB = I= BA as follows: First equate en- tries on the two sides of the equation AB = I. Then solve the resulting four equations for a, b, c, and d. Finally verify that BA = I as well.
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