ove that if AB = 1, then B = A- 2, 1 -1 21 and (b) 3 1 1 1 -2 1 2.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.2: Matrix Algebra
Problem 21EQ: Prove the half of Theorem 3.3 (e) that was not proved in the text.
icon
Related questions
Question
' I. (a) Prove that if AB = I, then B = A-1.
Use this result to find directly the inverses of
2,
1 -1
b11 b12
b21 b22/
3
2
(a)
and (b)
4
B =
and find
1
1
1
[Hint:
In (a) assume
-2
2
1
b11, b12, 621, b22-)
Transcribed Image Text:' I. (a) Prove that if AB = I, then B = A-1. Use this result to find directly the inverses of 2, 1 -1 b11 b12 b21 b22/ 3 2 (a) and (b) 4 B = and find 1 1 1 [Hint: In (a) assume -2 2 1 b11, b12, 621, b22-)
Expert Solution
steps

Step by step

Solved in 4 steps

Blurred answer
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elements Of Modern Algebra
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,