1.Consider the 2 functions f1(t) and f2(t);
1. f1(t) = { a1.e^ -2t for t>=0 and
= { 0 for t<0 }
f2(t) = { a2.e^ -t + a3.e^ -2t for t>=0 and
= { 0 for t<0 }
Find a1,a2 and a3 such that f1(t) and f2(t) are orthonormal on the interval 0 to infinity.
2. If Q is an n x n symmetric matrixand a1,a2 are such that 0 < a1I <

Please see the attached file for the fully formatted problems.
6. Perform the row operation (-2) R1 + R2 R2 on the matrix .
8. What are the dimensions of the matrices shown below?
a) b)
9. Find

Assistance with Matrices
Please see attachment.
Provide an example of a matrix that has no solution. Use row operations to show why it has no unique solution. Also, some matrices have more than one solution (in fact, an infinite number of solutions) because the system is undetermined. (In other words, there are not enough co

A system described in the attachment is under feedback control of the form u = Kx + r where r is the reference input.
(i) Show that (A,C) is observable.
(ii) Compute a K of the form {see attachment} so that (A - BK, C) is unobservable. (I.e., the closed loop system is unobservable)
(iii) Find the transfer function of the open