Question
Consider an n×n matrix A and a non-zero n×1 vector p. Their product Ap = α² p, where {α ∈ R ∉and α -1,0,1} . Based on the given information, the Eigen value of A² is :
Options :
α
α²
√α
α4
Answer :
α4
Solution :
If γ is the eigen value of A, then eigen values Am is λm
Ap = a2p ... eq (i)
We know that
AX = λX ... eq (ii)
On comparing eq (i) and eq (ii)
λ = a2
So the given value of matrix A is λ = a2
Eigen value of A2 = λ2 = a4
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