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Question

If A=201510013, the find A1 using elementary row operations.

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Solution

A=201510013
A=IA
201510013=100010001A
R112R1
⎢ ⎢1012510013⎥ ⎥=⎢ ⎢1200010001⎥ ⎥A
R2R25R1
⎢ ⎢ ⎢10120152013⎥ ⎥ ⎥=⎢ ⎢ ⎢12005210001⎥ ⎥ ⎥A
R3R3R2
⎢ ⎢ ⎢101201520012⎥ ⎥ ⎥=⎢ ⎢ ⎢120052105211⎥ ⎥ ⎥A
R32R3
⎢ ⎢ ⎢10120152001⎥ ⎥ ⎥=⎢ ⎢ ⎢12005210522⎥ ⎥ ⎥A
R2R252R3
⎢ ⎢1012010001⎥ ⎥=⎢ ⎢12001565522⎥ ⎥A
R1R1+12R3
100010001=3111565522A
A1=3111565522

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