MATH 3321
Sample Questions for Exam 3
1. Find
x
and
y
so that
±
2
x
4

35
x
²
+
±
3
y

2

2

y
²
=
±

52

51
2
²
.
2. Let
A
=
±
2

13
04

2
²
,B
=
±

31
25
²
,C
=
3

2
0

1
12
.
Perform the indicated operations, if possible: (a)
AC
(b)
AB
(c)
B
+
AC
(d)
CBA
3. Show that the matrix of coeﬃcients is nonsingular and use Cramer’s rule to ±nd the unique
solution of the system:
x
1

x
2
+
x
3
=1
2
x
2

x
3
2
x
1
+3
x
2
4. Write the system in the vectormatrix form
A
x
=
b
and solve by ±nding
A

1
.
2
x
1
+
x
2
=2
4
x
1
x
2
=

4
5. Write the system in the vectormatrix form
A
x
=
b
and solve by ±nding
A

1
.
x
1
+
x
2
2
x
1
x
2

x
3
=0
x
1
+2
x
3
=4
6. Given the set of vectors
{
u
=(1
,

2
,
1)
,
v
=(2
,
1
,

,
w
=(7
,

4
,
}
Is the set linearly dependent or linearly independent? If it is linearly dependent, express one
of the vectors as a linear combination of the other two.
7. Given the set of vectors
{
v
1
,
0
,

,
v
2
=(

3
,
1
,
2)
,
v
3
=(8
,

2
,

5)
,
v
4

9
,
1
,
}
Is the set linearly dependent or linearly independent? If it is linearly dependent, how many
independent vectors are there in the set?
1