You are a secret agent who has been given these three ...
Please Answer the following questions, some are multiple choice, others require some work.
1. Write the augmented matrix for the given system:
[pic]
2. Use the system in problem #1. Without interchanging any of the rows in the augmented matrix, what is the first value which will be replaced with zero when using the Gaussian Elimination method?
[pic]
| |a. |-1 |
| |b. |1 |
| |c. |3 |
| |d. |5 |
3. Represent the given matrix with a system of equations in x, y, and z.
[pic]
| |a. |[pic] |
| |b. |[pic] |
| |c. |[pic] |
| |d. |[pic] |
4. Use elementary row operations to write the matrix in echelon form:
[pic]
| |a. |[pic] |
| |b. |[pic] |
| |c. |[pic] |
| |d. |[pic] |
5. [pic][pic]Solve the system of equations by the Gaussian elimination method:
[pic]
6. Solve the system of equations by the Gaussian elimination method:
[pic]
7. [pic][pic][pic][pic]When solving the following system of equations by the Gaussian elimination method,
[pic]
which of the following is NOT a matrix leading to the solution?
[pic]
| |a. |[pic] |
| |b. |[pic] |
| |c. |[pic] |
8. Given A = [pic]and B = [pic], find A + B .
[pic]
| |a. |[pic][pic] |
| |b. |[pic] |
| |c. |[pic] |
| |d. |[pic] |
9. [pic][pic][pic][pic]Given A = [pic]and B = [pic], find A - B.
| |a. |[pic] |
| |b. |[pic] |
| |c. |[pic] |
| |d. |[pic] |
10. [pic][pic][pic][pic]Given A = [pic]and B = [pic], find A + B.
[pic]
| |a. |[pic] |
| |b. |[pic] |
| |c. |[pic] |
| |d. |[pic] |
11. Given A = [pic], find -3A
| |a. |[pic] |
| |b. |[pic] |
| |c. |[pic] |
| |d. |[pic] |
12. Given A = [pic]and B = [pic], find 2A - 3B.
[pic]
| |a. |[pic] |
| |b. |[pic] |
| |c. |[pic] |
| |d. |[pic] |
13. Find the product: [pic][pic]
[pic]
| |a. |[pic] |
| |b. |Undefined |
| |c. |[pic] |
| |d. |[pic] |
14. [pic][pic][pic][pic]Find the product: [pic][pic]
[pic]
| |a. |[pic] |
| |b. |[pic] |
| |c. |[pic] |
| |d. |Undefined |
15. [pic][pic][pic][pic]When finding the product, [pic][pic]how many pairs of numbers must be multiplied together?
[pic]
| |a. |3 |
| |b. |9 |
| |c. |12 |
| |d. |27 |
16. [pic][pic][pic][pic]For the product, [pic][pic]what will be the element in row 3, column 1?
[pic]
| |a. |8 |
| |b. |3 |
| |c. |0 |
| |d. |-4 |
17. Given these matrices and their dimensions: A3x2, B3x2, and C2x4 Which of the following can NOT be performed?
[pic]
| |a. |A+B |
| |b. |3C |
| |c. |AxB |
| |d. |AxC |
[pic][pic][pic][pic]FOR PROBLEMS 18 - 20 USE THESE MATRICES:
A = [pic]B = [pic]
18. Find A2,1
[pic]
| |a. |1 |
| |b. |2 |
| |c. |3 |
| |d. |4 |
19. [pic][pic][pic][pic]If C = AxB, the order of C is:
[pic]
| |a. |1x3 |
| |b. |3x1 |
| |c. |3x3 |
| |d. |unable to determine |
20. If C=AxB, find C2,1.
[pic]
| |a. |37 |
| |b. |30 |
| |c. |23 |
| |d. |21 |
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