Find the Inverse of the Matrix by Gauss-Jordan: [ 1 2 -9 , -2 -4 19, 0 -1 2 ] Pl

Question

Find the Inverse of the Matrix by Gauss-Jordan:

[ 1 2 -9 ,

-2 -4 19,

0 -1 2 ]

Please show work !

Explanation / Answer

[ 1 2 -9 |1 0 0] [ -2 -4 19|0 1 0] [ 0 -1 2 |0 0 1] apply R2--> R2 + 2R1 [ 1 2 -9 |1 0 0] [ 0 0 1 |2 1 0] [ 0 -1 2 |0 0 1] apply R3 -->R3 - 2R2 [ 1 2 -9 |1 0 0] [ 0 0 1 |2 1 0] [ 0 -1 0 |-4 -2 1] apply R2 R3 [ 1 2 -9 |1 0 0] [ 0 -1 0 |-4 -2 1] [ 0 0 1 |2 1 0] apply R1-->R1 + 2R2 [ 1 0 -9 |-7 -4 2] [ 0 -1 0 |-4 -2 1] [ 0 0 1 |2 1 0] apply R1-->R1 + 9R3 [ 1 0 0 |11 5 2] [ 0 -1 0 |-4 -2 1] [ 0 0 1 |2 1 0] apply R2-->R2*-1 [ 1 0 0 |11 5 2] [ 0 1 0 | 4 2 -1] [ 0 0 1 |2 1 0] A^-1 = [ 11 5 2] [ 4 2 -1] [ 2 1 0]

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