Math 2050
Sample problems for midterm test 2
July 2023
Instructor
Margo Kondratieva
PLEASE NOTE
The midterm is scheduled on
July 14 at 2pm in ED1020
. Duration 50 minutes.
1. Use a dark pencil or pen and write clearly to make the work legible.
2. Show all your work. Write your answers in the indicated spots.
3. Any calculators and books/notes are NOT permitted at the exam.
1. Express
⃗v
=
"
0
2
#
as a linear combination of the columns of
A
=
"
1
1
3
2
#
Answer
:
2. Is the following set of vectors linearly dependent or independent? Explain.
10
20
30
,
10
20
10
,
30
60
50
,
Answer
:
3. True or False?
(a) For any pair of 3X3-matrices
A
and
B
,
AB
̸
=
BA
.
(b) For all 3X3-matrices
A
and
B
, (
A
+
B
)
T
=
B
T
+
A
T
=
A
T
+
B
T
.
(c) Let A and B be two
N
×
N
-matrices,
N
≥
2, such that AB=0. Then either
A
= 0 or
B
= 0. Here 0 represents a zero
N
×
N
-matrix.
(d) For any four 3X3-matrices, (
ABC
)
D
=
A
(
BCD
).
4. Consider matrices
A
=
"
1
−
1
3
2
#
,
B
=
"
2
1
1
2
#
.
a) Find
AB
,
A
T
,
A
+
B
, and
2
AB
.
b) Find
X
given that
XA
=
X
+
B
.