Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Compute the determinant of the matrix by cofactor expansion.
1)
2–2 6 4
2 2 7 1
6–614 14
–2 2 –6 1
1)
A)
80
B)
–40
C)
–160
D)
–80
2)
4 1 5
5 4 3
4 1 4
2)
A)
–11
B)
11
C)
213
D)
–35
3)
–1 2 –1
4 3 –2
–3–4–1
3)
A)
–38
B)
38
C)
14
D)
24
4)
8 0 0
7–4 0
–4 2 2
4)
A)
–64
B)
50
C)
64
D)
–78
1
5)
4 1 2
–4–1–5
8 5 3
5)
A)
0
B)
–12
C)
36
D)
–36
Calculate the area of the parallelogram with the given vertices.
6)
(0, 0), (5, 8), (13, 10), (8, 2)
6)
A)
108
B)
54
C)
53
D)
59
Compute the determinant of the matrix by cofactor expansion.
7)
–5 5 –5 3
0 –1 2 –2
0 3 0 0
0 –3 1 4
7)
A)
150
B)
0
C)
–150
D)
–30
Solve using Cramer’s rule.
8)
2x1+ 6x2=32
4x1+x2= –2
8)
A)
(2, –6)
B)
(–6, –2)
C)
(–2, 6)
D)
(6, –2)
2
Determine the values of the parameter s for which the system has a unique solution, and describe the solution.
9)
2sx1+4x2= –3
2x1+ sx2= 4
9)
A)
s ±2; x1=–3s –16
2(s –2)(s +2) and x2=4s+ 3
(s –2)(s +2)
B)
s ±4; x1= –3s –16 and x2= 4s + 3
C)
s 2; x1=–3s +16
2(s –2)(s +2) and x2=4s – 3
(s –2)(s +2)
D)
s ±2; x1=–3s –16
2(s –2)(s +2) and x2=4s+ 3
2(s –2)(s +2)
Compute the determinant of the matrix by cofactor expansion.
10)
5 2 –2 5 –4
0 4 2 1 0
0 0 –2 3 7
0 0 0 –1–5
0 0 0 0 5
10)
A)
0
B)
200
C)
–200
D)
–100
Determine the values of the parameter s for which the system has a unique solution, and describe the solution.
11)
sx1–7sx2= 3
3x1–21sx2= 5
11)
A)
s
1; x1=14
3(s + 1) and x2=9+ 5s
21s(s + 1)
B)
s
1; x1=4
21(s – 1)(s + 1) and x2=9– 5s
21(s – 1)(s + 1)
C)
s
0, 1; x1=4
3(s – 1) and x2=9– 5s
21s(s – 1)
D)
s ± 1; x1=4
3(s + 1) and x2=9– 5s
21s(s + 1)
3
Solve using Cramer’s rule.
12)
2x1+ 3x2=28
3x1– 2x2=3
12)
A)
(–6, 5)
B)
(–5, –6)
C)
(5, 6)
D)
(6, 5)
Calculate the area of the parallelogram with the given vertices.
13)
(–1, –2), (3, 6), (5, 0), (9, 8)
13)
A)
80
B)
40
C)
39
D)
44
B
Compute the determinant of the matrix by cofactor expansion.
14)
7 5 9
4 5 7
6 3 4
14)
A)
39
B)
–459
C)
955
D)
–39
D
15)
1 2 5
4 8 12
–2 3 –1
15)
A)
–28
B)
14
C)
28
D)
56
D
4
C
16)
2 1–3 1
0 6–1 6
–4 4 5 4
–2 5 1 3
16)
A)
80
B)
–1
C)
1
D)
0
Solve using Cramer’s rule.
17)
4x1+ 2x2=34
–2x1+ 3x2= –5
17)
A)
(7, 3)
B)
(–3, 7)
C)
(3, 7)
D)
(–7, –3)
Compute the determinant of the matrix by cofactor expansion.
18)
6–9 7
0 1 1
0 0 –8
18)
A)
–48
B)
39
C)
48
D)
–57
5
Answer Key
Testname: C3
6