Matrix Inversion by Gaussian Elimination
Iff matrix A is invertible, then the reduced row-echelon form of [ A I ] is [ I A–1 ] .
The details are on page 54 of the textbook.
Example 2.3.3 (Textbook, page 59, exercises 2.3, question 2(c), modified)
Find the inverse of  and hence solve the linear system
x – z = 1
3x + 2y = –3
–x – y = 2
 
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