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Grade: 12th pass
        
If eigen values of martix A are 1,1,1 then find eigen values of A2+2A+3I
one month ago

Answers : (1)

Aditya Gupta
1670 Points
							
hello shivangi, consider the following theorem:
If l is an eigenvalue of A, P(l ) is an eigenvalue of P(A). Conversely, if m is an eigenvalue of P(A), m = P(l ) for some eigenvalue l of A.
so, here P(A)= A^2+2A+3I. using the converse of the above theorem, let m is an eigenvalue of P(A), then m = P(l ) or  m = l2+2l+3 for some eigenvalue l of A. but all the eigen values of martix A are 1,1,1 and hence p(l)= 1^2+2*1+3= 6
hence eigen values of A2+2A+3I are 6, 6, 6.
kindly approve :=)
one month ago
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