Math 250, Section 12 Homework 7Assigned February 12, 2015

Due February 19, 2015

Here and throughout all future homework assignments, all sections and problems will refer to the textby Spence, Insel, and Friedberg.

Recommended exercises:See the link on the Sakai resources for the list of recommended problems.Exercises to hand in:

1. Section 1.7: problem 60

2. Section 2.1: problem 26

3. Let

A =[

2 −3−4 6

], B =

[8 45 5

], C =

[5 −23 1

].

Verify that AB = AC (but note that B 6= C).

4. Give an example of two matrices A and B such that the product AB is defined and neither A nor Bis a zero matrix, but their product AB is a zero matrix.

5. Section 2.3: problem 3

6. Section 2.3: problem 4

7. Section 2.3: problem 26 (Also find E−1.)

8. Section 2.3: problem 28 (Also find E−1.)

9. Section 2.3: problem 30 (Also find E−1.)

10. Note that 7 2 10 3 −1−3 4 −2

−2 8 −53 −11 79 −34 21

=

1 0 00 1 00 0 1

(You do not need to prove this.) Use this fact to solve

7x1 + 2x2 + x3 = 213x2 − x3 = 5

−3x1 + 4x2 − 2x3 = −1

without using Gaussian elimination.

Instructor: Matthew Russell