Exercises for Chapter 1 and Section 3.4
Math 81, Fall 2015
Instructor: Dr. Doreen De Leon
Instructions:
Do all of the following problems.
Show all of your work for each problem.
1. Identify the type(s) of equation for each of the following.
(a) (x 2 + 1
Exercises for Sections 4.14.2, 4.7 (Intro)
Math 81, Fall 2015
Instructor: Dr. Doreen De Leon
Instructions:
Do all of the following problems.
Show all of your work for each problem.
1. Consider the set C(R) with the standard addition and scalar multipli
Exercises for Sections 3.3 and 3.5
Math 81, Fall 2015
Instructor: Dr. Doreen De Leon
Instructions:
Do all of the following problems.
Show all of your work for each problem.
1. Is it possible for a homogeneous system of equations to be inconsistent (i.e.
Exercises for Sections 3.13.2
Math 81, Fall 2015
Instructor: Dr. Doreen De Leon
Instructions:
Do all of the following problems.
Show all of your work for each problem.
1. Which of the following are in echelon form?
a.
b.
c.
d.
[ ]
[ ]
[ ]
[ ]
2 3 40
0
Exercises for Section 1.6
Math 81, Fall 2015
Instructor: Dr. Doreen De Leon
Instructions:
Do all of the following problems.
Show all of your work for each problem.
1. Identify the type(s) of equation for each of the
following.
a. 2xy + (x 2 + 2y 2 )y =
Exercises for Sections 4.3, 4.7 (Continued)
Math 81, Fall 2015
Instructor: Dr. Doreen De Leon
Instructions:
Do all of the following problems.
Show all of your work for each problem.
1. Is the set cfw_(4, 2, 2),(5, 4, 3),(4, 6, 5),(7, 9, 3) linearly
inde
1.
Compute the determinant of
A=
(
1 5
0
2 4 1
1 2 0
)
using cofactor expansion.
2. Find the determinant of the following matrices given that
 
a b c
d e f
g h i
a.

b.
 
c.

d.


a
b c
d
e f
5 g 5h 5i
a b c
g h i
d e f
a+ d b+ e c+ f
d
e
f
g
h
i
Exercises for Sections 4.14.2, 4.7 (Cont)
Math 81, Fall 2015
Instructor: Dr. Doreen De Leon
Instructions:
Do all of the following problems.
Show all of your work for each problem.
1. Let S = cfw_(x, y, z) z = x 2. Is S a subspace of R 3 ? Why or why n
Exercises for Sections 3.13.2
Math 81, Fall 2015
Instructor: Dr. Doreen De Leon
Instructions:
Do all of the following problems.
Show all of your work for each problem.
1. Which of the following are in echelon form?
a.
b.
c.
d.
[ ]
[ ]
[ ]
[ ]
2 3 40
0