Find the​ inverse, if it​ exists, for the given matrix. 2 0 5 0 -1 0 3 3 7

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 5E
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Find the​ inverse, if it​ exists, for the given matrix.
2 0 5
0 -1 0
3 3 7
Expert Solution
Step 1

According to the given information it is required to calculate the inverse of the given matrix.

Advanced Math homework question answer, step 1, image 1

Step 2

Inverse of a matrix exist if and only if determinant is non zero.

So, first find the determinant of the matrix A.

Advanced Math homework question answer, step 2, image 1

Step 3

Now, find the A-1.

consider the augmented matrix:

Advanced Math homework question answer, step 3, image 1

Step 4

Now, convert the matrix into identity by doing the operations:

Advanced Math homework question answer, step 4, image 1

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