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Find P^(-1), if it exists, given P=[[10,...

Find `P^(-1)`, if it exists, given `P=[[10,-2],[-5, 1]]`.

Text Solution

Verified by Experts

We can write the given matrix as
`[[10,-2],[-5,1]] = [[1,0],[0,1]]P`
Applying `R_2->R_2+1/2R_1`
`[[10,-2],[0,0]] = [[1,0],[1/2,1]]P`
From this, we can see that we can not convert matrix on left side to identity matrix.
`:. P^-1` does not exist.
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