Name(s):
Score:
Math 148 Lab Assignment 4: §9.1-9.2
Directions: You may work in groups of 2–3 to complete this assignment. Answer
each question completely. Show all work to receive full credit, and circle your
final answer.
1. Solve the linear system
5x − y + 2z = 6
x + 2y − z = −1
3x + 2y − 2z = 1
by finding the augmented matrix and performing Gaussian elimination. (Note: You
must indicate which operation(s) you perform in each step of your solution.)
1
2. Determine whether the linear system
x − 2y + z = 3
2x − 3y + z = 8
is overdetermined or underdetermined and solve the system by finding the augmented
matrix and performing Gaussian elimination. (Note: You must indicate which operation(s) you perform in each step of your solution.)
2
3. Let


3 1 4
A = −2 0 1
1 2 2

and
Compute the following:
(a) AB
(b) BA
(c) (2A)T − (3B)T
3

1
0 2
B = −3 1 1
2 −4 1
4. Let


2 1
A =  6 3
−2 4
and
2 4
B=
1 6
Verify that (AB)T = B T AT .
5. Determine whether each matrix is singular or nonsingular. Find its inverse, if it exists.
4 6
(a) A =
6 9
3 1
(b) B =
4 2
4