Download PC Study Guide--Sec. 6.1-6.3 Haggenmaker Spring 2012-2013

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PC Study Guide--Sec. 6.1-6.3
Haggenmaker
Spring 2012-2013
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
____
____
____
1. Which of the following matrices is singular?
a.
c.
b.
d.
2. Find the inverse matrix required to solve
.
a.
c.
b.
d.
3. What is B if
and
.
a.
c.
b.
d.
4. Which matrix is not in row-echelon form?
a.
b.
c.
d.
____
5. What is the solution of the system of equations shown?
a. (–1, 2, 1)
b. (1, –2, –1)
____
____
c. (–1, 2, –1)
d. (1, –2, 1)
6. Write a matrix equation for the given systems of equations.
a.
c.
b.
d.
7. Write the system of equations in triangular form using Gaussian elimination. Then solve the system.
–3x – 18y + 6z = 3
–3x + y + 4z = 40
–5x – 5y – 4z = –60
a. x = –2, y = 1, z = 8
b. x = 1, y = 3, z = 10
____
c. x = 0, y = 4, z = 12
d. x = 39 , y = –5 , z = 5
8. Write the augmented matrix for the system of linear equations.
–9w
–5x
–3w
–3w
a.
+x
+ 9y
– 6x
– 8x
+ 8y + 2z = –6
– 7z = 6
+ 4y + 9z = 4
+ y = –2
c.
b.
____
d.
9. Solve the system of equations.
10x + 24y + 2z = –18
–2x – 7y + 4z = 6
–14x – 48y + 26z = 42
a. x = –8, y = 2, z = 7
b. x = 7, y = 6, z = –10
____ 10. If A =
c. infinite solutions
d. no solution
and B =
, find
a.
c.
b.
d.
____ 11. If A =
and B =
.
, find AB.
a.
c.
b.
d. Not possible
____ 12. Determine whether
a. Yes
and
are inverse matrices.
b. No
____ 13. Find the inverse of P
, if it exists.
a.
c. P
b.
d.
____ 14. Find the determinant of C =
.
a. –30
b. –15
____ 15. Find the determinant of L =
a. 30
b. 22
does not exist.
c. 10
d. –18
.
c. –30
d. 10
____ 16. Solve the matrix equation by using inverse matrices.
a.
3
( , 12)
2
b. (8, 5)
c. (–2, 1)
d. (–2, 5)
____ 17. Use an inverse matrix to solve the system of equations, if possible.
5x + 4y + z = –73
3x – 6y + 3z = 45
–4x + 8y – z = –33
a.
b.
c. no solution
d.
____ 18. Use Cramer's Rule to find the solution of the system of linear equations, if a unique solution exists.
4x + 5y = –21
–2x – 4y = 6
a.
b. no unique solution
c.
d.
____ 19. Use Cramer's Rule to find the solution of the system of linear equations, if a unique solution exists.
–6x – y + 3z = 33
4x – 6y – 2z = –42
–2x – 10y + z = –18
a.
b.
c. no unique solution
d.
Short Answer
20. Write the system of equations in triangular form using Gaussian elimination. Then solve the system.
5x + 5y + 5z = 30
–6x – 2y + 2z = 24
x + 2y – 5z = –27
21. Write the augmented matrix for the system of linear equations.
6w
–8x
7w
–5w
+ 8x + 4z = 9
– y + 5z = 9
– y – 2z = –6
+ 4x – 8y = –2
22. Solve the system of equations.
9x + 12y – 39z = 6
12x + 20y – 68z = –8
–6x – 12y + 42z = 12
23. Use an inverse matrix to solve the system of equations, if possible.
–5x – 6y – 2z = –37
x + 7y + 2z = 11
–x – 6y – 6z = 11
24. Use Cramer's Rule to find the solution of the system of linear equations, if a unique solution exists.
–3x – 3y = 18
–5x – 5y = 30
25. Use Cramer's Rule to find the solution of the system of linear equations, if a unique solution exists.
4x + 5y – 3z = 71
4x + 5y – 3z = 71
3x – 9y + z = –62
PC Study Guide--Sec. 6.1-6.3
Answer Section
Haggenmaker
Spring 2012-2013
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
OBJ:
NAT:
ANS:
OBJ:
NAT:
ANS:
OBJ:
NAT:
ANS:
OBJ:
NAT:
ANS:
TOP:
ANS:
TOP:
ANS:
NAT:
ANS:
NAT:
ANS:
NAT:
ANS:
NAT:
ANS:
NAT:
ANS:
NAT:
ANS:
NAT:
ANS:
NAT:
D
C
B
B
A
D
6-1.1 Solve systems of linear equations using matrices and Gaussian elimination.
2
TOP: Multivariable Linear Systems and Row Operations
B
6-1.1 Solve systems of linear equations using matrices and Gaussian elimination.
2
TOP: Multivariable Linear Systems and Row Operations
A
6-1.1 Solve systems of linear equations using matrices and Gaussian elimination.
2
TOP: Multivariable Linear Systems and Row Operations
D
6-1.2 Solve systems of linear equations using matrices and Gauss-Jordan elimination.
2
TOP: Multivariable Linear Systems and Row Operations
B
OBJ: 6-2.1 Multiply matrices.
NAT: 1
Matrix Multiplication, Inverses, and Determinants
D
OBJ: 6-2.1 Multiply matrices.
NAT: 1
Matrix Multiplication, Inverses, and Determinants
B
OBJ: 6-2.2 Find determinants and inverses of 2x2 and 3x3 matrices.
1
TOP: Matrix Multiplication, Inverses, and Determinants
A
OBJ: 6-2.2 Find determinants and inverses of 2x2 and 3x3 matrices.
1
TOP: Matrix Multiplication, Inverses, and Determinants
D
OBJ: 6-2.2 Find determinants and inverses of 2x2 and 3x3 matrices.
1
TOP: Matrix Multiplication, Inverses, and Determinants
A
OBJ: 6-2.2 Find determinants and inverses of 2x2 and 3x3 matrices.
1
TOP: Matrix Multiplication, Inverses, and Determinants
D
OBJ: 6-3.1 Solve systems of linear equations using inverse matrices.
2
TOP: Solving Linear Systems Using Inverses and Cramer's Rule
A
OBJ: 6-3.1 Solve systems of linear equations using inverse matrices.
2
TOP: Solving Linear Systems Using Inverses and Cramer's Rule
C
OBJ: 6-3.2 Solve systems of linear equations using Cramer's Rule.
2
TOP: Solving Linear Systems Using Inverses and Cramer's Rule
C
OBJ: 6-3.2 Solve systems of linear equations using Cramer's Rule.
2
TOP: Solving Linear Systems Using Inverses and Cramer's Rule
SHORT ANSWER
20. ANS:
x = –3, y = 3, z = 6
OBJ: 6-1.1 Solve systems of linear equations using matrices and Gaussian elimination.
NAT: 2
TOP: Multivariable Linear Systems and Row Operations
21. ANS:
OBJ: 6-1.1 Solve systems of linear equations using matrices and Gaussian elimination.
NAT: 2
TOP: Multivariable Linear Systems and Row Operations
22. ANS:
(6 – z, –4 + 4z, z)
OBJ: 6-1.2 Solve systems of linear equations using matrices and Gauss-Jordan elimination.
NAT: 2
TOP: Multivariable Linear Systems and Row Operations
23. ANS:
OBJ: 6-3.1 Solve systems of linear equations using inverse matrices.
NAT: 2
TOP: Solving Linear Systems Using Inverses and Cramer's Rule
24. ANS:
OBJ: 6-3.2 Solve systems of linear equations using Cramer's Rule.
NAT: 2
TOP: Solving Linear Systems Using Inverses and Cramer's Rule
25. ANS:
OBJ: 6-3.2 Solve systems of linear equations using Cramer's Rule.
NAT: 2
TOP: Solving Linear Systems Using Inverses and Cramer's Rule
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