As an area of concentration on final exam EMT 202 on July 14, 2014, the following exercises serve as your guide. Final exams are close notes and books affair. Similar exercises will come out.

1. Find the product of matrices M and N.

M = [8 4 0 ; -2 6 -3; 0 -4 2] where M is a 3×3 matrix

N = [3 -5; 5 -6; -3 -7] N is a 3 x2 matrix

2. For matrix 3 x 3 matrix A,

A = [ 2 3 4 ; 4 1 6 ; 2 -2 4 ]

Find a) determinant of matrix

b) cofactor of matrix A

c) cofactor transpose of A

d) inverse of matrix A

3. Solve the values of x, y, and z using a) Gauss Jordan method B) Cramer’s rule

C) Gaussian elimination method d) LU Factorization

2x +2y-4z-4=0

2x+5y+8z -4=0

X+2y+4z-6=0

4. Solve the system of coupled first order DE using matrix method.

f1’(x) = 4 f1(x) +10 f 2 (x)

f2’(x) = 3f1(x) +5 f 2 (x)

where f1(0) = 2 f2(0) = 3

5. Find the eigenvalues and eigenvectors of a matrix [2 -5; 1 -4].

6. Find the modal and spectral matrices of the matrix A = [ 7 6; 6 2]

7. Find the dot and cross products of vectors a= 5i – 17j +12k and b= – 2i +4j – 6k.

8. Find the image of the line 2y – 3x = 4 under the translation [1 -2].

9. Find the modal matrix P and diagonal matrix using similarity transformation D = P -1 A P.

Matrix A = [ 2 -5; 1 -4]