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. Show that if A is an m n matrix, then AAT and AT A are sy
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
2 , v =
1
1 . It can be shown that
Problem 1. Let u =
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 matrix with two identical rows be invertible? Why or wh
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 contains an example of exactly how much work to show.
1. Solve
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 example of exactly how much work to show and how
to sh
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 following subset S1 a subspace of R2 ?
S1 =
IC
a1
a2
D
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 operations to solve the system.
1.
2 1
3 5
1
2
2.
1
2
3.