Math 4326
Spring 2013
Homework 2
Solutions
1 2 1 0
1. If A = 2 7 2 6 , nd a matrix P so that P A = R, where R is reduced.
1 4 1 12
Solution: We reduce from A to R, keeping track of the elementary row operation
at each stage, and use it to form the associa
Math 4326
Fall 2013
Homework 4
Solutions
Do the following problems from the book:
Section Problems
4.1
12, 14, 16, 32
4.2
4, 14, 24
Book problems
2s + 4t
2s
Section 4.1 Problem 12 Let W be the set of all vectors of the form
2s 3t . Show that
5t
4
W is
Math 4326
Fall 2013
Homework 5
Solutions
Do the following problems from the book:
Section 4.3 : 4, 14
Section 4.3
2
2
8
Problem 4 Do the vectors 1 , 3 , 5 form a basis for R3 ?
1
2
4
Solution: Lets generalize rst. Given vectors v1 , v2 , . . . , vm in R
Math 4326
Fall 2013
Homework 6
Solutions
Do the following problems from the book:
Section
Problems
4.5
8, 14, 18, 26
4.6
2, 10, 12, 20, 24
Section 4.5 Problem 8 Find the dimension of V = cfw_(a, b, c, d) : a 3b + c = 0.
Solution: The general rule of thumb