Math 261: Worksheet 4 (1.8, 1.9, 2.1)
1. Consider the linear transformation T represented by T (x) = Ax. Determine whether
T is one-to-one, onto, or neither.
1 2 0
(a) A = 0 1 1
0 0 1
1 2
(b) A = 0 1
Math 261: Worksheet 5/6 (2.2-2.5)
1. Find the transposes of the matrices
1 2
3 4
5 1
6 7 19
7 0 23 .
19 23 32
and
2. Consider
A=
1 1 2
2 0 1
and
3 0
B = 1 2 .
1 1
Verify that (AB)T = B T AT .
3. Sh
Worksheet 3
MATH 261-061, Linear Algebra, Winter 2017
Name:
In order to receive full credit, you must show all the necessary work for each problem,
and that work must be clear and organized.
7
3
5
Worksheet 5
Name:
Problem 1.
Use the Invertible Matrix Theorem to decide if the following are invertible:
5
7
A=
3 6
3
0
0
0
B = 3 4
8
5 3
3 0 3
4
C= 2 0
4 0
7
4
2
D=
6 3
Problem 2.
a) Can a square
Math 261: Worksheet 2 (1.1-1.4)
1. Solve the following systems of linear equations by using elementary row operations on
the corresponding augmented matrices.
(a)
3x1 2x2 = 19
x1 + x2 = 8
3x1 + 2x2 x3
Math 261: Worksheet 2 (1.5-1.6)
1. Solve the system of linear equations
x1 x2 + 3x3 = 0
.
2x1 + x2 + 3x3 = 0
2. Describe all solutions of Ax = 0 in parametric vector form, where A is row equivalent
to
Math 261
Sample Quiz 2
January 27, 2016
Name:
In order to receive full credit, you must show all the necessary work for each problem, and
that work must clear and organized.
Your HW assignment contain
HW 2
Math 261
January 27, 2016
Name:
In order to receive full credit, you must show all the necessary work for each problem, and
that work must clear and organized.
See the worked problem below for an
Lab Worksheet
Math 261
February 3, 2016
For this worksheet, you will practice demonstrating whether certain subsets of Rn are subspaces or not. Do this by following the proof template.
Problem: Is the
MAT 261 Linear Algebra with Applications
Worksheet 1: row reducing with no free variables
January 21, 2017
Consider each matrix as the augmented matrix of a linear system.
Perform the necessary row op