Q. 255.0( 6 Votes )

# <span lang="EN-US

Answer :

Given that Then (Expanding along R1)

Calculating the Cofactors of matrix A, we get

C11=-2, C12=5, C13=1

C21=0, C22=-2, C23=2

C31=2, C32=-1, C33=-1

Adjoint of a matrix A is defined as the transpose of Cofactor matrix of matrix A.

Hence,  Inverse of a matrix A is defined as a matrix A-1 such that

AA-1=I=A-1A.

A-1 is also equal to , |A|≠0.

Hence,  Given that

x + y + z=6

x+2z=7

3x+y+z=12

Hence Pre-multiplying with A-1 both sides, we get  or Hence x=3, y=1 and z=2.

Or

Given that We know that A=IA

Hence, Using R2R2+R1 Using  Using R1R1-2R2 and R3R3+2R2 Using R35R3 Using and  Here A-1A=I and hence Rate this question :

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