**REVIEW FOR FINAL EXAM -EMT 202**

** **There is nothing better than a good preparation for the upcoming final exam on July 1, 2013. Since topics are too wide, you must concentrate on the following areas of concentration as shown in the examples below. Study them thoroughly for similar exercises will come out on the final exam. Workbook/textbook and notes will be your references.

1. 1. Find the inverse matrix of C= 1 2 4

2 1 4

3 2 2

2. Solve by Cramer’s rule

2x-y+2z=2

x-2y+z=4

x+y+2z=1

3. 3. Solve by Gaussian elimination method

X+2y+z=1

3x-2y-3z=1

X+2y+2z=4

4. 4.Find the eigenvalues and eigenvectors of matrix

A= 2 4

1 1 2

5. 5. Find matrix P and diagonal matrix D with D = P^{-1} A P of matrix

A A = 3 4

2 1

6. 6. Solve the coupled differential equations:

F1’(x) = 2 f1(x) – 3 f2(x)

F’2(x) = 4 f1(x) + 3 f2(x)

7. 7.Find the dot or inner product **a.b** if a= [6, -3, 5] and b= [ 2, 4, 8 ] ^{T}, so that b is a column vector.

8. 8. Find the cross product of vectors U= (3, 2,1) and V= (1, -2, 2).

9. 9. Transform vector V =[ with transformation T(V) =[ . Graph.

10. 10. Find the image of the line y-x =4 under the translation. Graph.

## Stephen obele

/ June 26, 2013Good day sir

I did not see my Quiz scores

Thanks