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Math 2890-001

Spring 2018

Recommended Problems


These problems will not be collected, but I highly recommend that you look them over.

The homework can be done by hand, or using a calculator (handheld or online), or using a computer software program. See the Linear Algebra Software page for some options.


All of the problems below are taken from Linear Algebra and its applications (5/e) by David C. Lay with the exception of the problems for Section 6.3 and the last problem for Section 6.4.

A list of recommended problems for the 4th edition is also available if that is the edition you are using.

Chapter 1
Section 1.1 #5, 9, 15, 31, 33
Section 1.2 #1, 5, 7, 13, 15, 33
Section 1.3 #5, 9, 11, 13, 15
Section 1.4 #1, 3, 5, 9, 11, 25, 39
Section 1.5 #3, 11, 31
Section 1.7 #1, 15, 19, 31, 41
Section 1.8 #9, 10, 17, 19, 37, 39
Section 1.9 #37, 39
Chapter 1 Supplementary Exercises #6, 23, 24
Chapter 2
Section 2.1 #1, 5, 7, 11, 40
Section 2.2 #3, 33, 37
Section 2.3 #3, 5, 9, 43, 44, 45
Section 2.4 #1, 7, 24, 25
Section 2.5 #1, 11, 31
Section 2.8 #7, 9, 11, 13, 25, 37
Section 2.9 #11, 13, 23
Chapter 2 Supplementary Exercises #3, 13, 19
Chapter 6
Section 6.1 #1, 5, 11, 17
Section 6.2 #5, 9, 13, 21, 35
Section 6.3 (If you have trouble viewing this problem try using Firefox or download section_63.pdf.)
Let $y=\left(\begin{array}{r} 10 \\ 4 \\ 8 \end{array}\right)$ and let $W$ be the span of $\left(\begin{array}{r} 1 \\ 2 \\ 3 \end{array}\right) \text{ and } \left(\begin{array}{r} 3 \\ 4 \\ 1 \end{array}\right).$
#1. Find the vector in $W$ that is closest to $y$.
#2. Write $y$ as the sum of a vector in $W$ and a vector orthogonal to $W$.
Section 6.4 #3, 7, 9, 15, 25
(If you have trouble viewing this next problem try using Firefox or download section_64.pdf.)
Use Wedderburn rank reduction as shown in class to find the QDR factorization of the matrix $$A=\left(\begin{array}{rrr} -1 & 4 & 3 \\ -2 & 5 & 10 \\ -1 & 4 & 1 \\ 0 & 3 & -6 \end{array}\right).$$
Section 6.5 #3, 7, 15
Section 6.6 #1, 3, 11
Chapter 6 Supplementary Exercises #11, 17-20
Chapter 4
Section 4.9 #5, 7, 21
Chapter 5
Section 5.1 #5, 7, 13, 15, 39
Section 5.2 #1, 9, 13, 15
Section 5.3 #7, 9, 15, 17, 19
Section 5.5 #1, 5
Section 5.6 #1, 9, 11, 13, 15
Section 5.7 #3, 5
Section 5.8 #1-11 (odd), 17, 19, 21
Chapter 5 Supplementary Exercises #13-16
Chapter 7
Section 7.1 #11, 17, 19, 37
Section 7.2 #1, 3, 9
Section 7.3 #1, 3
Section 7.4 #5, 7, 9, 11, 15
Chapter 7 Supplementary Exercises #15, 16

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