9.

J= Integration of sqrt(1/(1-X^4)) from 0 to 1

K= Integration of sqrt(1/(1+X^4)) from 0 to 1

L= Integration of sqrt(1/(1-X^8)) from 0 to 1

Which of the following is true for the definite integrals shown above?

Ans: J<L<1<K

I used the histogram to guess the relationship but is there any way to calculate the exact value?

12.

Let A be a 2*2 matrix for which there is a constant k such that the sum of the entries in each row and each column is k. Which of the following must be an eigenvector of A?

Ans: (1 1)

I thought (1 0) and (0 1) are also appropriate, can any one help me clarify these questions?

Thanks.