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# If A=|[2,0,-1],[5,1,0],[0,1,3]| , then find A-1 using elementary row operations - CBSE (Commerce) Class 12 - Mathematics

ConceptElementary Operation (Transformation) of a Matrix

#### Question

If A=|[2,0,-1],[5,1,0],[0,1,3]| , then find A-1 using elementary row operations

#### Solution

|A|=|[2,0,1],[5,1,0],[0,1,3]|

=2(3-0)-0(15-0)-1(5-0)

=6-0-5

=1

≠0

Hence A-1 exists.

A-1A=1

A^(-1)[[2,0,-1],[5,1,0],[0,1,3]]=[[1,0,0],[0,1,0],[0,0,1]]

Applying R_1 ->(1/2)R_1

A^(-1)[[1,0,-1/2],[5,1,0],[0,1,3]]=[[1/2,0,0],[0,1,0],[0,0,1]]

Applying R_2->R_2+(-5)R_1

A^(-1)[[1,0,-1/2],[0,1,5/2],[0,1,3]]=[[1/2,0,0],[-5/2,1,0],[0,0,1]]

Applying R_3->R3+(-1)R_2

A^(-1)[[1,0,-1/2],[0,1,5/2],[0,0,1/2]]=[[1/2,0,0],[-5/2,1,0],[5/2,-1,1]]

Applying R_3->(2)R_3

A^(-1)[[1,0,-1/2],[0,1,5/2],[0,0,1]]=[[1/2,0,0],[-5/2,1,0],[5/2,-1,2]]

Applying R_1->R_1+(1/2)R_3 and R_2->R_2+(-5/2)R_3

A^(-1)[[1,0,0],[0,1,0],[0,0,1]]=[[3,-1,1],[-15,6,-5],[5,-2,2]]

A^-1 =[[3,-1,1],[-15,6,-5],[5,-2,2]]

Is there an error in this question or solution?

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Solution If A=|[2,0,-1],[5,1,0],[0,1,3]| , then find A-1 using elementary row operations Concept: Elementary Operation (Transformation) of a Matrix.
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