Math 2890-001

Fall 2017

Recommended Problems

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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.

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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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