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test2.pdf
Math 2318 - Test 2, Due back by July 20 at 11:59 pm
Questions are worth 5 points each
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Identify the indicated submatrix.
1) A = 0 1 -7 -5
7 -1 0 2
2 5 -2 0
. Find A12.
A) -5
2 B) 2 5 -2 C) 1 D) 7
1)
Find the matrix product AB for the partitioned matrices.
2) A = 4 0 1
2 -1 -3
5 3 7
, B = -2 0 8 5
1 6 2 2
4 -1 0 3
A)
-8 0 32 20
-5 -6 14 8
-7 18 46 31
B)
-4 -1 32 23
-17 -3 14 -1
21 11 46 52
C)
-4 -1 0 3
-12 -3 0 -9
28 -7 0 21
D)
-4 -1 32 23
-17 -3 14 -1
21 11 46 52
2)
Solve the equation Ax = b by using the LU factorization given for A.
3) A = 3 -1 2
-6 4 -5
9 5 6
, b = 6
-3
2
A = 1 0 0
-2 1 0
3 4 1
3 -1 2
0 2 -1
0 0 4
A) x = 49
-38
32
B) x = 22
-7
15
C) x = 10
-2
-13
D) x = 25
-58
51
3)
Find an LU factorization of the matrix A.
4) A = 3 -1
-18 9
A) A = 1 0
-6 1 3 1
0 -3 B) A =
1 0
3 1 -
6 -1
0 3
C) A = 1 0
6 1 -3 -1
0 -3 D) A =
1 0
-6 1 3 -1
0 3
4)
1
Determine the production vector x that will satisfy demand in an economy with the given consumption matrix C and
final demand vector d. Round production levels to the nearest whole number.
5) C = .4 .3
.1 .6 , d =
52
76
A) x = 3
25 B) x =
208
242 C) x =
44
51 D) x =
40
3
5)
Solve the problem.
6) Compute the matrix of the transformation that performs the shear transformation x → Ax for
A = 1 0.17
0 1 and then scales all y-coordinates by a factor of 0.63.
A)
2 0.17
0 1.63
B)
1 0.17
0 0.63
C)
0.63 0.1071
0 1
D)
1 0.1071
0 0.63
6)
Find the 3 × 3 matrix that produces the described transformation, using homogeneous coordinates.
7) (x, y) → (x + 5, y + 4) A)
5 0 0
0 4 0
0 0 1
B)
1 0 5
0 1 4
0 0 0
C)
1 0 5
0 1 4
0 0 1
D)
1 0 4
0 1 5
0 0 1
7)
Find the 3 × 3 matrix that produces the described composite 2D transformation, using homogeneous coordinates.
8) Rotate points through 45° and then scale the x-coordinate by 0.2 and the y-coordinate by 0.4.
A)
0.1 -0.2 2 0
0.1 2 0.2 0
0 0 1
B)
0.1 2 -0.1 2 0
0.2 2 0.2 2 0
0 0 1
C)
0 -0.2 0
0.4 0 0
0 0 1
D)
0.1 2 0.1 2 0
-0.2 2 0.2 2 0
0 0 1
8)
Find the 4 × 4 matrix that produces the described transformation, using homogeneous coordinates.
9) Translation by the vector (4, -7, -9)
A)
4 0 0 0
0 -7 0 0
0 0 -9 0
0 0 0 1
B)
1 0 0 4
0 1 0 -7
0 0 1 -9
0 0 0 1
C)
0 0 0 4
0 0 0 -7
0 0 0 -9
0 0 0 1
D)
1 0 0 -4
0 1 0 7
0 0 1 9
0 0 0 1
9)
Determine whether b is in the column space of A.
10) A = 1 2 -3
1 4 -6
-3 -2 5
, b = 3
2
-5
A) Yes B) No
10)
2
11) A = -1 0 2
5 8 -10
-3 -3 6
, b = -4
5
3
A) No B) Yes
11)
Find a basis for the null space of the matrix.
12) A = 1 0 -5 -2
0 1 7 -4
0 0 0 0
A)
1
0
-5
-2
,
0
1
7
-4
B)
-5
7
1
0
,
-2
-4
0
1
C)
1
0
0
, 0
1
0
D)
5
-7
1
0
,
2
4
0
1
12)
Find a basis for the column space of the matrix.
13) B = 1 -2 2 -3
2 -4 9 -2
-3 6 -6 9
A)
2
1
0
0
,
23
5
0
- 4
5
1
B)
1
2
-3
, 2
9
-6
C)
1
0
0
, 0
1
0
D)
1
2
-3
, -2
-4
6
13)
The vector x is in a subspace H with a basis β = {b1, b2}. Find the β-coordinate vector of x.
14) b1 = 1
-2 , b2 =
-5
3 , x =
17
-13
A)
-4
1
B)
-2
3
C)
2
-3
D)
-3
2
14)
15) b1 = 2
-2
4
, b2 = 6
1
-3
, x = 26
9
-23
A)
5
-2
B)
-2
5
0
C)
2
-5
D)
-2
5
15)
3
Determine the rank of the matrix.
16) 1 -2 2 -4
2 -4 7 -4
-3 6 -6 12
A) 2 B) 1 C) 3 D) 4
16)
17)
1 0 -3 0 4
0 1 -3 0 2
0 0 0 1 1
0 0 0 0 0
A) 4 B) 2 C) 3 D) 5
17)
Compute the determinant of the matrix by cofactor expansion.
18) -1 2 -1
4 3 -2
-3 -4 -1
A) 24 B) 14 C) -38 D) 38
18)
19) 6 -9 7
0 1 1
0 0 -8
A) 48 B) 39 C) -48 D) -57
19)
20)
-5 5 -5 3
0 -1 2 -2
0 3 0 0
0 -3 1 4
A) 150 B) 0 C) -150 D) -30
20)
4
