Consider the following row reduction. A = [[0 0 1],[0 3 0],[1 0 2]] --> [[1 0 2],[0 3 0],[0 0 1]] --> [[1 0 2],[0 1 0],[0 0 1]] --> [[1 0 0],[0 1 0],[0 0 1]] Using this row reduction,...

Consider the following row reduction.

A = [[0 0 1],[0 3 0],[1 0 2]] --> [[1 0 2],[0 3 0],[0 0 1]] --> [[1 0 2],[0 1 0],[0 0 1]] --> [[1 0 0],[0 1 0],[0 0 1]]

Using this row reduction, write A and A^-1as products of elementary matrices.

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A = [[0 0 1],[0 3 0],[1 0 2]] --> [[1 0 2],[0 3 0],[0 0 1]] --> [[1 0 2],[0 1 0],[0 0 1]] --> [[1 0 0],[0 1 0],[0 0 1]]

`E_1=[[0,0,1],[0,3,0],[1,0,2]]`

`E_2=[[1,0,2],[0,3,0],[0,0,1]]`

`E_3=[[1,0,2],[0,1,0],[0,0,1]]`

`A^(-1)=E_3E_2E_1`

`A=E^(-1)_1E^(-1)_2E^(-1)_3`

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