Find the inverse of the matrix using elementary matrices. [[2,0],[1,1]]

avissidep 2021-01-17 Answered
Find the inverse of the matrix using elementary matrices. [[2,0],[1,1]]
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Expert Answer

Cristiano Sears
Answered 2021-01-18 Author has 96 answers

Let the given matrix be,
A=[[2,0],[1,1]]
Now transform the given matrix in to unit matrix I by performing column reduction to get,
A=[[2,0],[1,1]]
=[[2,0],[1,1]](c1>c1c2)
=[[1,0],[0,1]](c1>1/2c1)
=I
Now, construct sequence of elementary matrices such that E2*E1 A=I
The column operation are,
E1=[[1,0],[0,1]](c1>c1c2)
=[[1,0],[1,1]]
E2=[[1,0],[0,1]](c1>1/2c1)
=[[1/2,0],[0,1]]
Then the inverse of the matrix by elementary matrices is given by:
A1=E1×E2
=[[1,0],[1,1]][[1/2,0],[0,1]]
=[[1/2,0],[1/2,1]]

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