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 :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

If <span lang="ENMathematics - Board Papers

Using matrices soMathematics - Board Papers

<span lang="EN-USMathematics - Board Papers

Using properties Mathematics - Board Papers

Using matrices, sMathematics - Board Papers

If A is square maMathematics - Exemplar

If <span lang="ENMathematics - Exemplar

The management coMathematics - Board Papers

If A is an invertMathematics - Board Papers

If <iMathematics - Board Papers