Could someone please explain the answers to me please TrueFa

Could someone please explain the answers to me, please.

True/False:

(a) Consider a matrix A R^2×2 with eigenvalues = 2, 3. There is one and only one solution to A²A^TA³A^T x = b for any b R².

(b) Consider a mass spring system with values of m, k, and b such that the system exhibits critical damping. Decreasing the mass will cause the solutions to oscillate, while overall they still decay.

(c) Given p(t), q(t), y1(t), y2(t) are real-valued and twice differentiable functions, if y(t) = y(t) + iy(t) is a solution to the differential equation y + p(t)y + q(t)y = 0 then y(t) = y1(t) + y2(t) is also a solution.

(d) For any natural number n, the n-by-n matrix with all entries equal to 1 has n distinct eigenvalues.

(e) There exists a 3-by-3 matrix with no real eigenvalues.

Answers are: T,F,T,F,F

THANKS!

Solution