Find the inverse using elementary row transformations: `[[3,0,-1],[ 2,3,0],[ 0 ,4 ,1]]`

Explanation

Given,A=`[[3,0,-1],[ 2,3,0],[ 0 ,4 ,1]]`

Let `A=I_3A`

Applying `r_1->1/3r_1` and `r_2->r_2-2r_1` and `r_2->1/3r_3`


`[[1,0,-1/3],[ 0,1,2/9],[ 0,4,1]]=[[1/3, 0, 0],[ -2/9, 1/3, 0],[0 ,0 ,1]]A`


Applying `r_3->r_3-4r_2` and `r_3->9r_3` and `r_1->r_1+1/3r_3`, also `r_2=r_2-2/9r_3`


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