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Find the inverse using elementary row...

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

Text Solution

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A=`[(2,-1, 3),( 1, 2 ,4),( 3, 1 ,1)]`
`A=IA`
So,
`[(2,-1, 3),( 1, 2 ,4),( 3, 1 ,1)]`=`[(1,0, 0),( 0, 1 ,0),( 0, 0 ,1)]A`
Applying `r1=1/2r1,r2=r2-2r1` and `r3=r3-3r1` we get,
`[(1,-1/2, 3/2),( 0, 5/2 ,5/2),( 0, 5/2 ,-7/2)]`=`[(1/2,0, 0),( -1/5,2 /5 ,0),( -3/2, 0 ,1)]A`
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