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Question

Find the inverse of each of the following matrices by using elementary row transformations:

31027

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Solution

A=3 102 7We knowA=IA 3 102 7=1 00 1 A3-2 10-7 2 7 =1-0 0-1 0 1 A [Applying R1R1-R2]1 32 7 =1 -10 1A 1 32-2 7-6 = 1 -10-2 1+2 [Applying R2R2-2R1]1 30 1 = 1 -1-2 3 A 1 3-30 1 = 1+6 -1-9 -2 3 A [Applying R1R1-3R2]1 00 1 = 7 -10-2 3AA-1= 7 -10-2 3

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