1 1 Consider the matrix A The inverse of A is a matrix A-1 9-1 = \[ c d] " a b] that satisfies Га b] [1 [1 01 A¹A I. Multiply out set it equal to cd9 -1 01 come up with a system of 4 equations for the unknowns a, b, c and d. Then solve that system of unknowns using basic algebra. Use the values you obtain to write down the inverse matrix: • and equate corresponding entries to A-1=
1 1 Consider the matrix A The inverse of A is a matrix A-1 9-1 = \[ c d] " a b] that satisfies Га b] [1 [1 01 A¹A I. Multiply out set it equal to cd9 -1 01 come up with a system of 4 equations for the unknowns a, b, c and d. Then solve that system of unknowns using basic algebra. Use the values you obtain to write down the inverse matrix: • and equate corresponding entries to A-1=
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.3: Matrix Algebra
Problem 8E
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![1 1
Consider the matrix A
The inverse of A is a matrix A-1
9-1
= \[ c d] "
a b]
that satisfies
Га
b] [1
[1 01
A¹A I. Multiply out
set it equal to
cd9
-1
01
come up with a system of 4 equations for the unknowns a, b, c and d. Then solve that system of unknowns
using basic algebra. Use the values you obtain to write down the inverse matrix:
•
and equate corresponding entries to
A-1=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdf909276-6ad3-4144-b98c-235c5a32e436%2F1632b73a-5372-470b-a518-e511d932aebf%2Ftvu5f7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1 1
Consider the matrix A
The inverse of A is a matrix A-1
9-1
= \[ c d] "
a b]
that satisfies
Га
b] [1
[1 01
A¹A I. Multiply out
set it equal to
cd9
-1
01
come up with a system of 4 equations for the unknowns a, b, c and d. Then solve that system of unknowns
using basic algebra. Use the values you obtain to write down the inverse matrix:
•
and equate corresponding entries to
A-1=
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