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Find the inverse of the matrix. 5 -1 4 1 135 1. A= 2. B= 244 1 - 11/

Find the inverse of the matrix. 5 -1 4 1 135 1. A= 2. B= 244 1 - 11/

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Advanced Math - Inverse of a Matrix

Solve the given equations by finding the inverse of a matrix. Example is in the second pic. 

Example Find the inverse A 2R₁ + R₂ 5R₁ + R3 Solution: We will use the augmented matrix to reduced row-echelon form. 2 0 1 1 0 0 1 0 1\2 12 00 -2 3 4 0 1 0 -2 3 4 0 1 0 -5 5 6 0 0 1 -5 5 6 0 0 1 R₂ R3 - R₂ + R3 30 R3 -R3 + R₁ -5/R3 + R₂ = A-1 = 1 0 1\2 1\200 0 3 5 1 10 0 5 17\2 5 2 0 1 1\2 0 0 1 0 1\2 0 1 5 3 13 1\3 0 0 1 17 10 1\2 0 1\5, 201 -234 -556 1 0 1\2 0 1 5 3 0 0 1\30 0 0 1 R₁ 1 0 1\2 1\2 00 0 1 5 3 13 13 0 1 0 0 -2 5 3 0 1 0 -8 17 - 10 0 0 1 5 10 6 Since the identity matrix I appears to the left we conclude the matrix to the right of the line is the inverse of A. -25-3 -8 17 5 - 10 - 10 1\2 0 0 13 13 0 1\61\3 1\5, 5 10 6 -
Transcribed Image Text:Example Find the inverse A 2R₁ + R₂ 5R₁ + R3 Solution: We will use the augmented matrix to reduced row-echelon form. 2 0 1 1 0 0 1 0 1\2 12 00 -2 3 4 0 1 0 -2 3 4 0 1 0 -5 5 6 0 0 1 -5 5 6 0 0 1 R₂ R3 - R₂ + R3 30 R3 -R3 + R₁ -5/R3 + R₂ = A-1 = 1 0 1\2 1\200 0 3 5 1 10 0 5 17\2 5 2 0 1 1\2 0 0 1 0 1\2 0 1 5 3 13 1\3 0 0 1 17 10 1\2 0 1\5, 201 -234 -556 1 0 1\2 0 1 5 3 0 0 1\30 0 0 1 R₁ 1 0 1\2 1\2 00 0 1 5 3 13 13 0 1 0 0 -2 5 3 0 1 0 -8 17 - 10 0 0 1 5 10 6 Since the identity matrix I appears to the left we conclude the matrix to the right of the line is the inverse of A. -25-3 -8 17 5 - 10 - 10 1\2 0 0 13 13 0 1\61\3 1\5, 5 10 6 -
Find the inverse of the matrix. 5 - 1 4 1 1 1. A= 2. B= 3 5 244 1 - 11
Transcribed Image Text:Find the inverse of the matrix. 5 - 1 4 1 1 1. A= 2. B= 3 5 244 1 - 11
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