Q23 of 45 Page 1

Using properties of determinants, prove the following:


OR


Find the inverse of the following matrix using elementary operations :


Let’s Take L.H.S

L.H.S =




Taking x, y and z common from R1 , R2 and R3 in the second determinant






Applying R2 - >R2 - R1 and R3 - >R2 - R1 , we get



Taking (y - x)(z - x) then , we get



Now, Expanding along Coloumn1




Hence, Proved


OR


Given, A =


To find: Find the inverse of the A


Explanation: We have given, A =


We know, A = IA


Where I is the Identity Matrix



Applying R2 - >R2 + R1



Applying R2 - > R2 + 2R3



Applying R1→R1 - 2R2 and R3→R3 + 2R2



Applying R1→R1 + 2R3




Hence, This is the inverse of Matrix


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