Download to earn any credit, you must show work.

Prof. Israel N. Nwaguru
MATH 1324
CHAPTER 6 - REVIEW
WORK OUT EACH PROBLEM NEATLY AND ORDERLY BY SHOWING ALL THE STEPS AS
INDICATED IN CLASS ON SEPARATE SHEET, THEN CHOSE THE BEST ANSWER.
TO EARN ANY CREDIT, YOU MUST SHOW WORK.
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Use the Gauss-Jordan method to solve the system of equations.
1) 5x - 2y = 28
10x - 4y = 56
Answer:
28 2
+ y, y
5
5
2) 5x + 2y + z = -11
2x - 3y - z = 17
7x - y = 12
Answer: No solution
3) x - y + z = 8
x+ y+ z=6
3x + y + 3z = 10
Answer: No solution
4) 2x - 5y + z = 11
3x + y - 6z = 1
5x - 4y - 5z = 12
Answer:
29z + 16 15z - 31
,
,z
17
17
5) 3x + y + z = 5
4x + 5y - z = -8
10x + 7y + z = 2
Answer:
-6z + 33 7z - 44
,
,z
11
11
6) x - y + 3z = -8
x + 5y + z = 40
5x + y + 13z = 10
Answer: No solution
7) x + y + z = 7
x - y + 2z = 7
2x + 3z = 15
Answer: No solution
1
8) -2x - y - 8z = -37
+ 2z = 36
5x
8y + z = 11
Answer: (6, 1, 3)
9) 8x - 6y - z = -23
x - 2y + 2z = -12
-2x + y + z = 2
Answer: (4, 9, 1)
10) x - y + 4z = -12
+ z = -2
4x
x + 5y + z = 18
Answer: (0, 4, -2)
11) x + y + z = 1
x - y + 2z = -3
5x + y + z = -15
Answer: (-4, 3, 2)
Solve the problem.
12) The matrices give points and rebounds for five players in two games. Find the matrix that gives the
averages.
Points Rebounds
14
13
16
11
F=
8
9
4
7
6
15
Hurd
Spencer
Payne
Wayne
Boyd
Points Rebounds
10
11
14
9
S = 10
13
8
17
8
7
Hurd
Spencer
Payne
Wayne
Boyd
Answer:
12 12
15 10
9 11
6 12
7 11
2
13) Carney and Dobler sell home and mortgage insurance. Their sales for the months of May and June are
given in the matrices.
Home Mortgage
M=
J =
22,000 45,000
Carney
18,000 27,000
Dobler
25,000 42,000
Carney
14,000 21,000
Dobler
Find the matrix that would give the change in sales from May to June.
Answer:
3000 -3000
-4000 -6000
14) What is the size of the matrix?
8 4 -8 9
-2 12 3 -2
-3 0 -5 17
Answer: 3 × 4
15) What is the size of the matrix?
7 -7 5 -4
-8 -9 -4 -9
-10 0 -5 17
Answer: 3 × 4
16) What is the size of the matrix?
12
-11
8
Answer: 3 × 1
17) What is the size of the matrix?
3 -8 9 7
Answer: 1 x 4
Perform the indicated operation where possible.
-1 6 -9
3 -5 0
18) 1 6 -4 - 1 -1 -8
-6 2 11
5 -6 2
Answer:
-4 11 -9
0 7 4
11 -8 -9
3
19) -1 0 - -1 6
62
31
Answer:
0 -6
3 1
20) -2 7 3 - 4 3
Answer: Not defined
21) 4 4
+ -4
6
Answer: Not defined
22) -2 1 + 6 2
25
1 -1
Answer:
43
34
Perform the indicated operation.
23) Let A = 3 3 and B = 0 4 . Find 4A + B.
-1 6
26
Answer:
12 16
7 30
Find the order of the matrix product AB and the product BA, whenever the products exist.
24) A is 4 x 2, B is 4 x 2.
Answer: AB is nonexistent, BA is nonexistent.
25) A is 2 x 1, B is 1 x 1.
Answer: AB is 2 x 1, BA is nonexistent.
26) A is 2 x 1, B is 1 x 2.
Answer: AB is 2 x 2, BA is 1 x 1.
Given the matrices A and B, find the matrix product AB.
-6 8 -1
-1 -9 8
27) A = -7 7 9 , B = 2 -5 4 . Find AB.
-1 -7 -9
Answer:
6 -4 -5
16 18 -11
75 -8 -73
-67 80 9
4
30
28) A = 1 3 -2 , B = -2 1
2 0 4
04
Find AB.
Answer:
-3 -5
6 16
29) A = -1 3 , B = 0 -2 4
54
1 -3 2
Answer:
Find AB.
3 -7 2
4 -22 28
Determine whether the two matrices are inverses of each other by computing their product.
.5 .5
30) 9 -2 , - 7 - 9
7 -2
4 4
Answer: No
31) 5 3 and 2 -3
-3 5
32
Answer: Yes
Find the inverse, if it exists, of the given matrix.
32) A = -3 -6
-6 -1
Answer:
1
2
33 11
-
33)
2
11
1
11
51
24 5
Answer:
5 -1
-24 5
Solve the matrix equation for X.
34) A = -1 3 , B = -1 6 , AX = B
-10 4
42
Answer:
-2 0
-1 2
5
35) A = 5 8 , B = 3 , AX = B
35
7
Answer:
-41
26
Solve the system by using the inverse of the coefficient matrix.
36) x - y + 5z = -1
+ z = -1
4x
x + 4y + z = -17
Answer: (0, -4, -1)
37) x - y + z = 12
x+y+z= 2
x + y - z = -2
Answer: (5, -5, 2)
Determine whether the given ordered set of numbers is a solution of the system of equations.
38) (-1, 3, -3)
2x - 5y + z = -20
+ 5z = -18
3x
x + 2y - 2z = 11
Answer: Yes
39) (-5, 6)
3x + y = -9
4x + 3y = -2
Answer: Yes
Write an augmented matrix for the system of equations.
+ 4z = 24
40) 4x
8y + 3z = 28
8x + 4y + 3z = 36
Answer:
4 0 4 24
0 8 3 28
8 4 3 36
41) 2x + 4y + 8z = 38
3x + 6y + 4z = 49
7x + 4y + 3z = 68
Answer:
2 4 8 38
3 6 4 49
7 4 3 68
6
42) 6x + 3y = 24
5y = 10
Answer:
6 3 24
0 5 10
Write the system of equations associated with the augmented matrix. Do not solve.
1 0 0 -4
43) 0 1 0 7
001 3
Answer: x = -4
y= 7
z= 3
100 5
44) 0 1 0 8
0 0 1 -7
Answer: x = 5
y= 8
z = -7
Perform row operations on the augmented matrix as far as necessary to determine whether the system is
independent, dependent, or inconsistent.
45) x + y - 2z = 8
3x + z = - 6
2x - y + 3z = -14
Answer: Dependent
46)
x + y + z = 11
x - y + 3z = 5
2x + 2y + 2z = 15
Answer: Inconsistent
47) x - y + 3z = -17
+ z = -4
3x
x + 5y + z = 21
Answer: Independent
Write a matrix to display the information.
48) A bakery sells three types of cakes. Cake I requires 2 cups of flour, 2 cups of sugar, and 2 eggs. Cake II
requires 4 cups of flour, 1 cup of sugar, and 1 egg. Cake III requires 2 cups of flour, 2 cups of sugar, and 3
eggs. Make a 3 x 3 matrix showing the required ingredients for each cake. Assign the cakes to the rows and
the ingredients to the columns.
Answer:
222
411
223
7