MATH 320
Quiz 2
Discussion
Spring 2016
Tue, March 15
Name:
Section:
You have 15 minutes. Please write neatly and justify your answers.
Answers without justication will receive no credit.
1
- Scratch paper -
2
SCORE:

1. Let
5
A = −5
4e

3 −9
−3 10 .
5e 9e
(a) Calculate the determinant of
/8
(2 + 2 + 1 = 5 pts)
A.

(b) Consider the column vectors of
A:
v1

5
= −5 ,
4e

v2

3
= −3 ,
5e
v3
 
−9
=  10  .
9e
Determine whether they
are linearly dependent or independent.
(c) Consider the row vectors of
A:
w1 = 5 3 −9 , w2 = −5 −3 10 , w3 = 4e 5e 9e .
Determine whether they are linearly dependent or independent.
(1 + 2 = 3 pts)
2. You don't have to justify your answer for part (a).
(a) True or False: If the vectors
v1 , v2 , v3
in
R3
are linearly dependent then every vector
vj
must be a
linear combination of the other two vectors.
(b) Let
V
be the set of all vectors
a subspace of
(x, y, z, w)
in
R4
4
R .
3
such that
xy = zw.
Determine whether or not
V
is