Question

If-1,23 are eigen values of A then eigen values of A are

Answer 1

Suppose 'a' is an eigenvalue of A.

We know ,in linear algebra ,

Ax = ax , where ,a is an eigenvalue of A.

For power of A we have, A^(n)x = a^(n)x.

That means whatever be the power of A, the same will be the power of ,a,which is the eigenvalue of A.

Hence, A^(99)= 1^(99) =1 ,for eigenvalue 1.

A^(99)= 2^(99) for eigenvalue 2.

A^(99)=3^(99) for eigenvalue 3.

1^(99),2^(99),3^(99) are the eigenvalues of A^(99).

Hope this will help.

Cheers!!

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