For the matrix `A=[[3, 2], [1, 1]]`
, find the numbers `a`
and `b`
such that `A^2+a A+b I=O`
. Hence, find `A^(-1)`
.
Text Solution
Verified by Experts
We have, `A=[[3,1],[2,0]]`
then `|A|=1!=0`
`∴ A^(−1)` exists.
Now `A^2=A.A=[[3,1],[2,0]][[3,1],[2,0]]=[[11,4],[8,3]]`
`=>[[11,4],[8,3]]+a[[3,1],[2,0]]+b[[1,0],[0,1]]=[[0,0],[0,0]]`
`=> [[11+3a+b,4+a],[8+2a,3+a+b]]+[[0,0],[0,0]]`
Equating the corresponding elements, we get
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