M340L, Linear Algebra

This page is always under construction, so
you
should check it regularly. Assignments with the word **homework**
in **bold
face** are set in stone. Other assignments are still tentative.
Homework is generally due every Thursday in class, with the first assignment
due on January 28.

**Homework # 1:** (due January 28) Lots of problems, but they're short.

Section 1.1 (page 11) 7, 8, 14,
23, 24. On the true/false, you don't have to recite chapter and verse
when a statement is true, but your should justify your answers
somewhat.

Section 1.2 (page 25) 5, 10, 12, 15, 22, 23, 24

Section 1.3 (page 37) 12, 13, 23, 27

**Homework # 2:** (due February 4) Even more problems, but they're still
short.

Section 1.4 (page 47) 8, 12, 13, 17, 19, 24, 32

Section 1.5 (page 55) 8, 12, 24

Section 1.7 (page 71) 8, 10, 14, 22, 23

Section 1.8 (page 80) 7, 9, 18, 19, 22

**Homework # 3:** (due February 11)

Section 1.9 (page 90) 7, 8, 13, 23, 26

Supplemental exercises (page 102) 3, 10, 13. (We talked a lot about going from
the RREF to the set of solutions. Problem 13 is doing the reverse.)

Section 2.1 (page 116) 1, 2, 17, 27, 28

Section 2.2 (page 126) 2, 7, 9, 10, 31

There is no homework due on February 18. However, you should work some of the problems on Homework 4 as preparation for the midterm.

**Homework # 4:** (due February 25)

Section 2.2 (page 126) 35, 37, 38

Section 2.3 (page 133) 4, 8, 11, 12, 16, 17, 28, 39

Section 3.2 (page 199) 22, 24, 26, 28

**Homework # 5:** (due March 4)

Section 4.1 (page 223) 2, 4, 6, 8, 16, 18, 23, 24

Section 4.2 (page 234) 5, 8, 16 (there's more than one answer!),
25, 26, 28, 31.

**Homework # 6:** (due March 11)

Section 4.3 (page 243) 4, 5, 10, 14, 16, 21, 22

Section 4.4 (page 253) 1, 6, 10, 13, 15, 18, 28

Section 4.5 (page 260) 3, 7, 10, 14, 19

**Homework # 7:** (due March 25)

Section 4.5 (page 260) 21, 23, 30

Section 4.6 (page 269) 2, 4, 12, 17, 18, 19, 26

Section 4.7 (page 276) 1, 4, 6, 8, 13, 14, 20a

**Homework # 8:** (due April 1)

Section 5.1 (page 308) 1, 6, 10, 21, 22, 27, 31

Section 5.2 (page 317) 4, 10, 14, 17, 19, 21

Section 5.3 (page 325) 2, 4, 6, 13, 21

Note that the book's definition of the characteristic polynomial is
slightly different from the one I gave in class. The book says is it
det(A - &lambda I), while I defined it to be det(&lambda I - A). If the
matrix is m by m, then these definitions disagree by a factor of
(-1)^{m}. In answering the questions of section 5.2, use whichever
definition you prefer. My definition is the standard usage of the term, but
there are advantages to the book's definition, too. See the
wikipedia
page.

There is no homework due on April 8. However, the first 2/3 of homework #9 is best worked BEFORE the midterm, as the midterm will include material from sections 5.4 and 5.5

**Homework #9:** (due April 15)

Section 5.4 (page 333) 1, 5, 8, 12, 16, 17

Section 5.5 (page 341) 4, 7, 10, 16, 23, 24, 28. For problem 16, you can either
use the real and imaginary parts of the eigenvector with eigenvalue a-bi (as
in the book), or the imaginary and real parts of the eigenvector with eigenvalue
a+bi (as in lecture). For problem 28, use MATLAB to find the eigenvalues and
eigenvectors.

Section 5.6 (page 352) 2, 3, 4, 10.

**Homework #10:** (due April 22)

This week's homework has two parts. The first half includes the
following problems from the
book:

Section 5.6 (page 352) 12, 14, 17ab, 18a

Section 5.7 (page 361) 1, 6, 8, 12, 13, 14

The second half is posted here.
Solutions to the second half will be posted here after
5PM on Thursday.

**Homework #11:** (due April 29)

This week's assignment is entirely from the book.

Section 6.1 (page 382) 9, 14, 19, 20, 24, 26, 28

Section 6.2 (page 392) 6, 9, 12, 13, 23, 24

Section 6.3 (page 400) 2, 5, 7.

**Homework #12:** (due May 6)

Section 6.3 (page 400) 12, 14, 21, 22

Section 6.4 (page 407) 1, 4, 10, 11

Section 6.5 (page 416) 2, 4, 5, 17, 18

Section 6.6 (page 425) 1, 2, 4, 9

This homework must be turned in
promptly **in class** on Thursday
to receive credit. If you turn it in later that
day, there will not be time for the grader to get to it,
and I will not accept it.