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Find the inverse of the following matrix 2 3 0 1 4 6 ol

Find the inverse of the following matrix 2 3 0 1 4 6 ol

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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Question
Find the inverse of the following matrix 1 2 3 0 1 4 15 6 ol use this format: (show what is done to the rows) (A|In). Let us see an example. Suppose that 1 2 -3 A = 2 5 -8 -3 -5 8 First we make the super augmented matrix 1 1 0 0 2 -3 -8 2 5 0 1 0 -3 -5 8 0 01/ Now apply Gaussian elimination. Multiply the first row by -2 and 3 and add them to the second and third row. 1 0 0 1 2 -3 | 0 1 -2 -2 10 0 1 -1 | 3 01 Now multiply the second row by -1 and add it to the third row to get 1 2 -3 1 0 1 -2 0 0 1 1 0 -2 1 0 5 -1 1, This completes the Gaussian elimination. Now we continue Gauss Jor- dan elimination Multiply the third row by 2 and 3 and add it to the second and first row, to get 1 2 0 16 -3 3 0108 -1 2 0 0 1 5 -1 1, The last step is to multiply the second row by -2 and add it to the first row, 1000-1 0108-1 2 0015-1 The inverse matrix is B 8 = -1 2 5 -1 One can check that indeed AB = BA = 13.
Transcribed Image Text:Find the inverse of the following matrix 1 2 3 0 1 4 15 6 ol use this format: (show what is done to the rows) (A|In). Let us see an example. Suppose that 1 2 -3 A = 2 5 -8 -3 -5 8 First we make the super augmented matrix 1 1 0 0 2 -3 -8 2 5 0 1 0 -3 -5 8 0 01/ Now apply Gaussian elimination. Multiply the first row by -2 and 3 and add them to the second and third row. 1 0 0 1 2 -3 | 0 1 -2 -2 10 0 1 -1 | 3 01 Now multiply the second row by -1 and add it to the third row to get 1 2 -3 1 0 1 -2 0 0 1 1 0 -2 1 0 5 -1 1, This completes the Gaussian elimination. Now we continue Gauss Jor- dan elimination Multiply the third row by 2 and 3 and add it to the second and first row, to get 1 2 0 16 -3 3 0108 -1 2 0 0 1 5 -1 1, The last step is to multiply the second row by -2 and add it to the first row, 1000-1 0108-1 2 0015-1 The inverse matrix is B 8 = -1 2 5 -1 One can check that indeed AB = BA = 13.
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