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Question

Which of the following would be the Inverse of the matrix A found using Elementary Row Transformations where

A =∣ ∣131011361∣ ∣


A

5+323213+31

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B

5+323213+31

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C

5+323213+31

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D

5+323213+31

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Solution

The correct option is C

5+323213+31


We know, for matrix A,

A = IA

I = PA

P=A1

=∣ ∣131011361∣ ∣

A = IA

Lets convert the LHS into a Identity Matrix and apply the same transformations on the identity matrix on the right. The final matrix obtained in the right will give the inverse.

∣ ∣131011361∣ ∣=∣ ∣100010001∣ ∣A.

R3R33R1∣ ∣131011032∣ ∣=∣ ∣100010301∣ ∣A.

R3R3+3R2 then R1R13R2∣ ∣102011001∣ ∣=∣ ∣1300103+31∣ ∣A

R2R2R3 then R1R1+2R3∣ ∣100010001∣ ∣=∣ ∣5+323213+31∣ ∣A

I=A1AA1=5+323213+31


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