1. ECE 313: Home Work # 2 (due Sept. 26, 2006 before class)
1. Visit and read about how to use Cramer’s rule to solve a system of linear equations.(Use Matlab)
Apply the rule to solve:
3X1 + 4X2 + X3 + 2X4 = 22
2X1 + X2 + 3X3 + X4 = 17
X1 + 3X2+ 2X3 +2X4 = 21
4X1 + 2X2 + X 3+ X4 = 15.
2. Find the eigenvalues and unit-eigenvectors of the following matrix:

2. A matrix A is said to be Hermitian if AT = A. where
A matrix A is said to be Hermitian if AT = A* where * denotes conjugation. Show that for every choice of vector x, the scalar (called a Hermitian form):
H = x*TAx
is a real number.
4. MATLAB Problem:
y(x) = 12x x x x
Where -1 ≤ x ≤ 1.
Find the even part and the odd part of the polynomial y(x).
What are the even unit vectors (remember Cosineman)?
What are the odd unit vectors (remember Sineman)?
What is the DC value?
For N=2, 5, 10 develop the coefficients of the even and odd unit vectors.
Plot on the same graph the even part of y(x) and the 2, 5 and 10 term expansions of the even part.
Repeat for the odd part.
Finally add the DC to the N=2, 5, 10 term expansions of the even part plus the equivalent expansion of the odd part and on the same graph plot the odd part of y(x) and the above sum for the three N cases.
Describe what you observe. Were Sineman and Cosineman right? Was Fourier right?