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- What are the dimensions of matrix A?
- Construct a generic 3 by 4 matrix, B, using the correct subscripted
notation. (Hint: The element in the upper left corner is b11.)
-
- Put the following information into a 2 by 3 matrix and label it.
Keith scored 94 on his test and had a 99 homework average. Juan received 75
on his test and averaged 80 on homework. Yolanda's homework average was 90,
but she scored 70 on the test.
- Transpose the matrix in problem 3a and attach labels.
- Consider the matrices
- What is A + B?
- What is AT + B?
- If matrix B is symmetric does A + B = A + BT? Why or why not?
- To raise money, our high school band decided to sell candy. They sold
candy with nuts (N) and plain chocolate (P). Hoping to inspire people to
sell candy, the band director held a contest among the grade levels to see
which grade would sell the most candy. The contest lasted for 3 weeks. Here
are the results from the first two weeks. The numbers represent packages
sold:
- How much of each kind of candy had each grade level sold by the end of the second week?
- Which grade level was leading the contest?
- By the end of the third week, the totals were:
How much of each kind of candy did each grade level sell during the third
week?
- How many packages of plain chocolate were sold during the three-week
period by the band?
- If the band makes 30 cents profit from each package of candy with
nuts and makes 20 cents profit from each package of plain chocolate, how
much profit did each grade level make? Answer this question using matrices.
- How much total profit did the band make from this venture? Please
write your answer in dollars.
- Consider the following matrices:
- Is AB defined? If yes, what is it? If no, why not?
- Using two of A, AT, B, and BT form a product that is a
2 by 2 matrix. For instance, AAT is a 2 by 2 matrix. Find two more examples of this.
- For
find AB.
- Solve this system of equations using Gauss-Jordan elimination:
| x1 |
+ |
3x2 |
- |
x3 |
|
= |
|
-2 |
| 2x1 |
+ |
3x2 |
+ |
x3 |
|
= |
|
2 |
| 3x1 |
+ |
6x2 |
+ |
x3 |
|
= |
|
3 |
- Solve this system of equations using Gaussian elimination:
| 4x1 |
+ |
2x2 |
- |
x3 |
|
= |
|
-8 |
| 3x1 |
- |
x2 |
+ |
2x3 |
|
= |
|
-3 |
| x1 |
|
|
+ |
5x3 |
|
= |
|
8 |
- Find the inverse of this matrix:
- Does the inverse of a matrix always exist? Explain.
- Find the determinant of these matrices. Show your work when possible.
-
-
-
-
- Identify the following as consistent or inconsistent. If the system is consistent, further categorize it as underdetermined or uniquely determined. Explain.
- Ax = b where
-
| 2x1 |
+ |
3x2 |
+ |
x3 |
|
= |
|
10 |
| 4x1 |
+ |
2x2 |
|
|
|
= |
|
10 |
| 3x1 |
+ |
2x2 |
+ |
4x3 |
|
= |
|
20 |
-
| 7x1 |
+ |
7x2 |
+ |
11x3 |
|
= |
|
10 |
| x1 |
+ |
2x2 |
+ |
3x3 |
|
= |
|
4 |
| 4x1 |
+ |
x2 |
+ |
2x3 |
|
= |
|
3 |
- Ax = b where
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