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 :

  1. α

  2. α²

  3. √α

  4. α4

Show Answer

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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