Math 353 Linear Algebra Homework Problems

Below are the required homework problems from each section covered in the textbook. Homework should be scanned and uploaded to the appropriate section assignment.

Chapter 1
1.1:  1, 3, 7, 9, 11, 13, 15, 25, 27, 37, 39, 47, 53, 55.
1.2:  11%, 13%, 17%, (19-21)*, (22-24)*, 25, 27, 31, 35, 37, 43%, 45%.
1.3:  1, 3, 5, 9, 17.

Chapter 2
2.1:  5, 9, 15, 17, 19, 21, 25, 29, 33, 37, 39, 43, 45, 49, 51, 57, 59.
2.2:  7, 9, 11, 17, 19, 23, 25, 27, 29, 31, 35, 39, 41, 45.
2.3:  1, 5, 7, 11, 13, 15, 17, 31, 33, 37, 41, 45, 47, 55.
2.5:  1, 3, 5, 7, 9, 11.
2.6:  1, 3, 5, 7.

Chapter 3
3.1:  1, 3, 5, 9, 13, 15, 19, 21, 27, 31, 33, 39, 41.
3.2:  1, 3, 5, 7, 11, 13, 15, 21%, 23%, 25, 27, 33, 35.
3.3:  1, 3, 7, 9, 13, 15, 19, 21, 23, 25, 27, 31, 33, 43#, 45#, 49#.
3.4:  1, 3, 5, 9, 13, 17, 19.

Chapter 4
4.1:  1, 3, 5, 7, 9, 11, 13, 15, 19, 21, 27, 29, 43, 47.
4.2:  1, 3, 7, 11, 13, 15, 19, 21, 23, 25, 29, 33, 41.
4.3:  1, 3, 7, 9, 13, 15, 19, 31, 35, 37, 39, 41.
4.4:  1, 3, 5, 9, 15, 19, 23, 27, 29, 33, 37, 41, 43, 53, 55.
4.5:  9, 11, 13, 17, 21, 23, 25, 39, 41, 43, 47, 49, 53, 57, 59, 61, 65, 71, 73, 75.
4.6:  3, 5, 7, 9, 15, 21, 23, 25, 27, 31, 37, 41, 45, 51, 57, 61.
4.7:  1, 3, 5, 7, 9, 11, 13, 17, 19, 21, 23, 37, 39, 45, 47.

Chapter 5
5.1:  1, 3, 7, 9, 13, 19, 21, 23, 35, 39, 43, 45, 47, 49, 53, 57, 59, 65, 71.
5.2:  1, 7, 9, 13, 19, 23, 29, 35, 45, 47, 49, 57, 59, 71, 75, 90#.
5.3:  1, 3, 5, 15, 19, 23, 25, 33, 37, 51, 59.
5.4:  5, 7, 9, 11, 17, 19, 21, 25, 29, 31, 33.

Chapter 6
6.1:  1, 3, 9, 11, 13, 17, 25, 27, 29#, 33, 36, 37, 41, 43, 55.
6.2:  1, 3, 5, 9, 11, 13, 15, 19, 21, 25, 29, 41, 43, 45, 51, 53.
6.3:  1, 3, 5, 7, 9, 11, 15#, 17#, 21, 23%, 25%, 29, 31, 33, 35, 37, 43.
6.4:  1, 3, 5, 11, 13, 15, 17, 19, 21, 23.
6.6:  1, 2, 3, 7, 11, 23, 25, 27, 29, 31, 39, 41, 45, 47, 55, 57, 59, 61, 63.

Chapter 7
7.1:  2, 3, 9, 11, 15, 17, 21, 23, 25, 27, 41, 43, 45%.
7.2:  1, 3, 5, 7%, 9%, 11%, 17, 19, 23, 25, 27, 29.
7.3:  7, 11#, 15#, 19, 23, 25, 33, 35, 39, 41, 43, 47, 51%.
7.4:  1, 3, 7, 9.

Problems marked with % have a note below:
1.2 #11, 13, 17:  The given matrix is the augmented matrix of the system. The book does not include the vertical line before the right-hand-side terms.
1.2 #43, 45:  The given matrix is the coefficient matrix of the system.
3.2 #21, 23:  You don't have to verify with software/graphing utility.
6.3 #23, 25:  You don't have to verify with software/graphing utility.
7.1 #45:  Part (c) is very easy once you have done Section 7.2.
7.2 #7, 9, 11:  The book tells you where you have already found the eigenvalues and eigenvectors for these matrices in the homework from Section 7.1. You can use your answer from 7.1 on these problems without doing all of that work again.
7.3 #51:  This problem is really long. Sorry.

Problems marked with # have a hint below:
3.3 #43, 45, 49:  You do not have to find all 5 determinants the long way. You do not even have to calculate the matrices for each part. You can find all of these determinants by just finding |A| and then using rules of determinants.
5.2 #90:  Show that the dot product of the given vectors is 0.
6.1 #29:  First write (4,2,0) as a linear combination of the vectors (1,1,1), (0,-1,2), and (1,0,1) (one could show that those three vectors form a basis for ℝ3).
6.3 #15, 17:  See Section 6.1 Example 7 for a reminder of what the standard matrix for a rotation in ℝ2 looks like.
7.3 #11, 15:  Since the matrices are symmetric, you do not actually have to find any eigenvectors to know the dimension of the eigenspaces.

Groups of problems marked with * count as one problem for grading purposes.