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If A(0) = [[2 ,-2,-4],[-1,3,4],[1,-2,-3]...

If `A_(0) = [[2 ,-2,-4],[-1,3,4],[1,-2,-3]] and B_(0) =[[-4,-4,-4],[1,0,1],[4,4,3]]` and `B_(n) = adj (B_(n-1)),n inN` and `I` is an dientity matrix of order 3. For a variable matrix X, the equation `A_(0) X = B_(0)` will heve

A

unique solution

B

infinite solution

C

finitrly many solution

D

no solution

Text Solution

Verified by Experts

The correct Answer is:
D
`because A_(0) = [[2,-2,-4],[-1,3,4],[1,-2,-3]] rArr abs(A_(0)) = 0`
and abj `B_(0) = [[-4,1,4],[-3,0,4],[-3,1,-3]]^(T) = [[-4,-3,-3],[1,0,1],[4,4,3]]=B_(0) `
`because B_(n) = adj (B_(n-1)), n in N `
`therefore B_(1) = adj (B_(0) )=B_(0)`
`rArr B_(2) = adj (B_(1)) = adj (B_(0)) = B_(0),`
`B_(3) = B_(0) , B_(4) = B_(0) , ...`
`therefore B_(n) = B_(0) AA n in N`
`because abs(A_(0)) = 0`
`rArr A_(0)^(-1)` is not possible
Hence, System of equation `A_(0) X = B_(0)` has no Sol.
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