Linear Algebra Unit 3 Worksheet Spring 2015
Name(s): BE Y
You may use the backs of these pages for additionai workspace, or attach work papers as needed.
I . Compute the determinant either by observation (justify your answer) or cofactor
expansion. N0 c
MATH 2010 Linear Algebra
Unit 3 Homework Assignment 2 (13pts)
2
0
0
5.1-1 Does Ax = 2x have a nontrivial solution? Ax = x Ax 2x = ( A 2 I 2 ) x = ;
3 2
1 0 1 2 rref 1 2
A 2I2
=
=
2 0 1 3 6 0 0 ; the system has a free variable and
3 8
therefore has
Linear Algebra
Unit 3 Worksheet
Fall 2015
Name(s):_
You may use the backs of these pages for additional workspace, or attach work papers as needed.
1. Compute the determinant either by observation (justify your answer) or cofactor
expansion. No calculator
MATH 2010 Linear Algebra
Unit 2 Homework Assignment 3
2.8-1 H is the set of all vectors (points) in the 1st quadrant. Let x = (1,1). Clearly x is in H, but
1 x = (1, 1) is in the third quadrant and clearly not in H. Thus H is not closed under
scalar multi
MATH 2010 Linear Algebra
Unit 2 Homework Assignment 1
2
T (= Au
u) =
0
2
T (= Av
v) =
0
1.8-1
0 1 2 1 + 0 (3) 2
=
=
2 3 0 1 + 2 (3) 6
0 a 2 a + 0 b 2a
=
=
2 b 0 a + 2 b 2b
1.8-3 In other words, solve Ax = b. Augment and row reduce!
1 0 3 2
MATH 2010 Linear Algebra
Unit 1 Homework Assignment 1
1.1-4 Find the point of intersection of the lines x1 + 2 x2 = and 3 x1 2 x2 =
13
1
Write as an augmented matrix and use elementary row operations.
1 2 13
1 2 13 1
1 2 13
3 2 1 3R1 + R 2 R 2 0 8 40 8 R
MATH 2010-080 Linear Algebra
Fall 2015
Instructor: James McCoy
Office Location: OMNI 91 (2nd floor, across the hall from OMN 289)
Phone: (423) 697-3389
E-Mail: Please contact me using the internal email system of our eLearn course website
Class Meeting Ti
MATH 2010-80 Linear Algebra
Fall 2015 TR 11:00-12:15 pm
Week
Dates (Mon-Fri)
1
24-Aug to 28-Aug
2
31-Aug to 4-Sep
3
7-Sep to 11-Sep
4
14-Sep to 18-Sep
5
21-Sep to 25-Sep
6
28-Sep to 2-Oct
7
5-Oct to 9-Oct
8
12-Oct to 16-Oct
9
19-Oct to 23-Oct
10
26-Oct to
MATH 2010 Linear Algebra
Worksheet: Subspaces, Basis, Column Space, Null Space, and Dimension (Sections 2.8-2.9)
Names:
Linear Algebra Section 2.8 Worksheet: Subspaces, Basis, Column Space and Null Space
1.
Is the following a subspace of n for the indicat
Chattanooga State Technical Community College
Mathematics and Sciences Division
Semester Syllabus
MATH 2010 Linear Algebra
Credit Hours: 3
Class Hours: 3
CATALOG COURSE DESCRIPTION:
An introduction to topics in linear algebra including linear systems, mat
MATH 2010 Linear Algebra
Unit 1 Review Worksheet Answer Key (Sections 1.1-1.5, 1.7)
Names:
3 4 4
6
2 1 6 , b = 2 , and let W = Spancfw_a , a , a , where a , a , a are the columns of A.
Let A =
1
2
3
1
2
3
1 3 2
4
1. Is b in W? Show your work (
Linear Algebra Test #3 Review
3.1, 3.2, 3.3, 5.1, 5.2, 5.3
1. Use one of the techniques we discussed in class to evaluate the following determinants.
3
0
(a) 4 5
0 2
2
7
6
4 0
7 1
(c)
2 6
5 8
1 3 5
(b) 2 1 1
3 4 2
0 0
0 0
3 0
4 3
2. Determine the values o
MATH 2010 Linear Algebra
Unit 1 Review Worksheet (Sections 1.1-1.5, 1.7)
Names:
3 4 4
6
2 1 6 , b = 2 , and let W = Spancfw_a , a , a , where a , a , a are the columns of A.
Let A =
1
2
3
1
2
3
1 3 2
4
1. Is b in W? Show your work (no calculat
Linear Algebra Test #3 Review Answer Key
1. -32
2. For s 0,
1
4
, the system has a unique solution described by x1 =
1
6s 2
.
, x2 =
2
12 s 3
12 s 3s
3. A is not invertible when a = - 27. (Not invertible when detA=0)
4. a. 8
b. 16
c. 16
d. -32
5. -11a + 5
Math 2010
Test 2 Review
Fall 2015
1.8-1.10, 2.1-2.3, 2.8-2.9
1.
1 0 1
Let A =
, and define T : R 3 R 2 by T(x) = Ax.
3 5 4
1
a. Find the image of u = 2 under T.
3
6
b. Find a vector x whose image under T is b = .
17
c. Find all x such that T(x) =
Math 2010
Test 2 Review Answer Key
Spring 2015
1.8-1.10, 2.1-2.3, 2.8-2.9
6
b. 7
0
1
1.4
c. x = x3
1
1.
2
a.
5
2.
18
T (-2u +3v ) =
20
3.
0 1
a.
1 0
4.
2
5
1 3
A=
3
6
5.
1 2 4
A=
0 3 6
6.
a = -2, b = 3
7.
Size of matrix B is 5 x 6
Section 1.10 Linear Models in Business, Science, and Engineering
Read the portions in the text on Linear Equations and Electrical Networks and Difference Equations (p
82-85. Then complete BOTH of the problems below.
1. For the figure below, write a matrix
MATH 2010 Linear Algebra
Chapter 5 Case Study
Due Thu 11/17/15
Name(s): _
These problems come from sections 1.10 and 5.6 in the textbook, or are based on material from
those sections. If you do not have the book partner with someone who does. Please write
Linear Algebra Section 1.5 Solution Sets of Linear Systems
Homogeneous Systems: A system is homogeneous if it can be written as Ax = 0 .
A homogeneous system is always consistent since x = 0 is a solution.
x = 0 is called the trivial solution.
We want t
Linear Algebra Section 1.4 Matrix Equations
Throughout Section 1.4, let A be an m n matrix with columns a1 , a 2 , , a n .
This can also be written as A = [a1 , a 2 , , a n ] .
Definition: If A is an m n matrix with columns a1 , a 2 , , a n and x is in n
Linear Algebra Section 1.1 Systems of Linear Equations
Intro:
A linear equation in the variables 1 , , is an equation that can be written in the form
1 1 + 2 2 + + = ,
where and the coefficients 1 , , are real or complex numbers that are usually known in
Linear Algebra Section 1.3 Vector Equations
What is a vector?
2 is the set of all vectors with exactly 2 real number entries.
3 is the set of all vectors with exactly 3 real number entries.
n is the set of all vectors with exactly n real number entries
Linear Algebra Section 1.2 Row Reduction and Echelon Form
Echelon and Reduced Echelon Form of a Matrix:
Note that matrices do NOT NECESSARILY represent systems of equations, but the method of row
reduction will be the same.
A rectangular matrix is in eche