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प्रश्न
Find the inverse of the matrix A=`[[1,2],[1,3]]` using elementry transformations.
उत्तर
A=`[[1,2],[1,3]]`
|A|=3-2
=1≠ 0
∴`A_1` exists
We have `A=A^-1=I`
`[[1,2],[1,3]]A^1`=`[[1,0],[0,1]]`
Applying` R_2→R_2-R_1`
`[[1 ,2],[0,1]]A^1=[[1,0],[-1, 1]]`
Applying `R_1→R_1-2R_2`
`[[1,0],[0,1]]A^1=[[3,-2],[-1 ,1]]`
Hence `A^-1=[[3,-2],[-1,1]]`
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