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

Question
Matrices asked 2021-01-17
Find the inverse of the matrix using elementary matrices. $$[[2,0],[1,1]]$$

## Answers (1) 2021-01-18
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,
$$A=[[2,0],[1,1]]$$
$$=[[2,0],[1,1]](c_1 -> c_1 - c_2)$$
$$=[[1,0],[0,1]](c_1 -> 1/2 * c_1)$$
=I
Now, construct sequence of elementary matrices such that E2*E1 A=I
The column operation are,
$$E_1=[[1,0],[0,1]](c_1 -> c_1 - c_2)$$
$$=[[1,0],[-1,1]]$$
$$E_2=[[1,0],[0,1]](c_1 -> 1/2 * c_1)$$
$$=[[1/2,0],[0,1]]$$
Then the inverse of the matrix by elementary matrices is given by:
$$A^(-1)=E_1xxE_2$$
$$=[[1,0],[-1,1]]*[[1/2,0],[0,1]]$$
$$=[[1/2,0],[-1/2,1]]$$

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