   Chapter 11.3, Problem 8E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# 7 − 8 ■ The inverse of a 2 × 2 Matrix: Find the inverse of a matrix and verify that A − 1 A = A A − 1 = I 2 and B − 1 B = B B − 1 = I 3 . B = [ 1 3 2 0 2 2 − 2 − 1 0 ]

To determine

To Find:

To find the inverse of the given matrix B= and to verify that B1B=BB1=I3.

Explanation

Approach:

If we take a 3×6 matrix with left half as matrix B and right half as I3 and transform the left half into identity matrix by performing elementary row operations on the entire matrix, the right half becomes inverse of the matrix B.

If A is a square matrix of dimension n×n and there exist another square matrix B of dimension n×n such that AB=I=BA, then we say B is the inverse of A.

Calculation:

As observed in the previous question; B=

Take a matrix of dimension 3×6 with left half as matrix B and right half as I3 and perform row operations to transform the left half into I3.

=...R3R3+2R1=...R212R2=...R3R35R2=...R1R13R2=......R3R3=......R1R1+R3=......R2R2R3

Thus, B1=.

Verification:

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