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Assignment Hw1fall14 due 09/03/2014 at 10:56pm CDT
1.
ft-uiowa-math2550
• Two lines intersecting in a point
• Two parallel lines
• Two lines that are the same
(1 pt) Library/WHFreeman/Holt linear algebra/Chaps 1-4-
/holt 01 02 007.pg
Determine if the matrix


−2 −3
1 −1 0
 0
0 −5
1 0 
0
0
1
0 0
is in echelon form, reduced row echelon form, or neither.
Choose the most appropriate answer.
Answer: ? .
5. (1 pt) Library/TCNJ/TCNJ LinearSystems/problem1.pg
Determine whether the following system has no solution, an infinite number of solutions or a unique solution.
Correct Answers:
• not in echelon form
? 1.
2.
(1 pt) Library/WHFreeman/Holt linear algebra/Chaps 1-4/holt 01 02 006.pg
? 2.
Determine if the matrix


1 −8 0
3
8
 0
0 1 −4 −4 
0
0 0
0
0
is in echelon form, reduced row echelon form, or neither.
Choose the most appropriate answer.
Answer: ? .
? 3.
+5y
+4y
+11y
+15y
−6y
−18y
+5y
+4y
+11y
= 5
= 7
= 23
=
15
= −6
= −18
= 5
= 7
= 25
Correct Answers:
• Unique Solution
• Infinite Solutions
• No Solution
Correct Answers:
• reduced row echelon form
3.
−6x
−4x
−10x
−10x
4x
12x
−6x
−4x
−10x
(1 pt) Library/WHFreeman/Holt linear algebra/Chaps 1-4-
/holt 01 02 010.pg
Determine if the matrix

6. (1 pt) Library/TCNJ/TCNJ LinearSystems/problem3.pg
Give a geometric description of the following systems of equations

1 9 0 6 0
 0 0 1 3 0 
0 0 0 0 1
is in echelon form, reduced row echelon form, or neither.
Choose the most appropriate answer.
Answer: ? .
? 1.
Correct Answers:
• reduced row echelon form
? 2.
4. (1 pt) Library/TCNJ/TCNJ LinearSystems/problem11.pg
Give a geometric description of the following systems of equations.
? 1.
? 2.
? 3.
7x
6x
4x
8x
4x
8x
+
+
+
+
+
+
7y
5y
4y
8y
4y
8y
? 3.
= −6
=
8
= 6
= 13
= 6
= 12
−4 x − 16 y
3 x + 12 y
7 x + 28 y
x − 3y =
2x − 3y =
7x − 9y =
x − 3y =
2x − 3y =
7x − 9y =
= −4
=
3
=
7
5
9
31
5
9
28
Correct Answers:
• Three identical lines
• Three lines intersecting at a single point
• Three non-parallel lines with no common intersection
Correct Answers:
1
10. (1 pt) Library/TCNJ/TCNJ LinearSystems/problem17.pg
Determine whether the following system has no solution, an infinite number of solutions or a unique solution.
7. (1 pt) Library/TCNJ/TCNJ LinearSystems/problem2.pg
Determine whether the following system has no solution, an infinite number of solutions or a unique solution.
? 1.
? 2.
? 3.
−7 x + 2 y + 6 z =
−9 x + 5 y + 7 z =
−15 x − 20 y + 15 z
6x + 8y − 6z
−15 x − 20 y + 15 z
6x + 8y − 6z
3
10
=
0
= −3
= 0
= 0
? 1.
? 2.
Correct Answers:
? 3.
• Infinite Solutions
• No Solution
• Infinite Solutions
? 4.
8. (1 pt) Library/TCNJ/TCNJ LinearSystems/problem4.pg
Give a geometric description of the following system of equations
? 1.
? 2.
? 3.
2x + 4y − 6z
−x + 5y − 9z
2x + 4y − 6z
−3x − 6y + 9z
2x + 4y − 6z
−3x − 6y + 9z
=
=
=
=
=
=
12
1
12
16
−12
18
11.
(1 pt)
/solve RREF 2.pg
9. (1 pt) Library/TCNJ/TCNJ LinearSystems/problem6.pg
Give a geometric description of the following systems of equations
? 3.
? 4.
The solution is (
)
Three
Three
Three
Three
=
=
=
=
=
=
=
=
=
=
=
=
−5
5
22
0
8
0
6
15
−18
−5
5
25
Library/Rochester/setAlgebra35SystemMatrices-
,
,
,
,
,
,
Correct Answers:
• -9--5*(x2)-1*(x3)--5*(x4)-0*(0-1*(-5-1*(9--6*(x8))--6*(x8))
• x2
• x3
• x4
• 0-1*(-5-1*(9--6*(x8))--6*(x8))-1*(9--6*(x8))--6*(x8)
• -5-1*(9--6*(x8))--6*(x8)
• 9--6*(x8)
• x8
6x − 9y + 6z = 3
10 x − 15 y + 10 z = 5
12 x − 18 y + 12 z = 6
x + 2y + 8z = 1
x + 3 y + 10 z = 0
4 x + 8 y + 28 z = 3
−5 x + 3 y −
z = −3
−4 x + 2 y +
z =
2
11 x − 5 y − 5 z = −11
−5 x + 3 y −
z = −3
−4 x + 2 y +
z =
2
11 x − 5 y − 5 z = −8
12. (1 pt) Library/TCNJ/TCNJ RowReduction/problem10.pg
If the following system has infinitely many solutions,
7x
−9 x
−11 x
Correct Answers:
•
•
•
•
z
z
3z
21 z
17 z
8z
2z
5z
6z
z
z
3z
Given the augmented matrix below, solve the associated system
of equations. For your variables, use x1, x2, x3, x4, x5, x6, x7,
and x8.


1 −5 1 −5 0 7 −8
4 −9
 0
0 0
0 1 1
1 −6
0 


 0
0 0
0 0 1
1 −6 −5 
0
0 0
0 0 0
1 −6
9
• Two planes intersecting in a line
• Two parallel planes
• Two planes that are the same
? 2.
+
+
+
+
−
+
+
+
−
+
+
+
Correct Answers:
• No Solution
• Unique Solution
• Infinite Solutions
• Infinite Solutions
Correct Answers:
? 1.
−3 x −
y
−4 x − 2 y
−13 x − 7 y
5 x + 15 y
−4 x − 13 y
2x + 6y
10 x + 2 y
25 x + 5 y
−30 x − 6 y
−3 x −
y
−4 x − 2 y
−13 x − 7 y
identical planes
planes intersecting at a point
planes intersecting in a line
planes with no common intersection
then k =
− 5y
+ 2y
−
y
,h=
Correct Answers:
• 19
• -8
2
− 4z = 5
− 2z = 7
+ hz = k
16. (1 pt) Library/Utah/College Algebra/set11 Systems of Equations and Inequalitie
13. (1 pt) Library/ma112DB/set11/sw7 3 21.pg
Given the system of equations
/1050s11p4.pg
The solution of the linear system
x + y + z = −2,
y − 3z = −4,
2x + y + 5z = 1,
(a) determine whether the system is inconsistent or dependent;
Your answer is (input inconsistent or dependent)
(b) if your answer is dependent, find the complete solution.
Write x and y as functions of z.
x=
y=
=
=
=
=
4
13
−15
31
,s=
r=
,t=
,u=
.
Correct Answers:
•
•
•
•
• inconsistent
•
•
2
1
-5
6
17. (1 pt) Library/Utah/College Algebra/set11 Systems of Equations and Inequalitie
/1050s11p5.pg
14. (1 pt) Library/TCNJ/TCNJ RowReduction/problem5.pg
Suppose that the following
+ 8y
+ 28 y
+ 16 y
+ u
+ 4u
− u
+ 2u
is
Correct Answers:
6x
21 x
12 x
+ s + t
+ 2s + 3t
− s + 2t
+ 2s − 3t
r
r
r
r
The solution of the linear system
+ s + t
+ 2s + 3t
− s + 2t
+ 2s − 3t
r
r
r
r
= 2
= k
= 4
is a consistent system. Then k =
Correct Answers:
+ u
+ 4u
− u
+ 2u
−1
−11
−1
13
=
=
=
=
is
• 7
r=
,s=
,t=
,u=
.
Correct Answers:
15. (1 pt) Library/Utah/College Algebra/set11 Systems of Equations and Inequalities• 5
• -2
• -4
• 0
/1050s11p3.pg
The principle that you process the coefficient matrix only
once is so important that we need to practice some more. This
and the next two problems all have the same coefficient matrix.
You want to process it just once, unless you enjoy retracing your
steps.
The solution of the linear system
r
r
r
r
+ s + t
+ 2s + 3t
− s + 2t
+ 2s − 3t
+ u
+ 4u
− u
+ 2u
18.
(1 pt) Library/WHFreeman/Holt linear algebra/Chaps 1-4/holt 01 01 003.pg
Determine which of the points (2, 4), (5, 5), and (−3, 3) lie on
both the lines −x1 + 3x2 = 10 and −x1 + 5x2 = 18.
Answer:
−14
−35
−1
−17
=
=
=
=
Correct Answers:
• (2,4)
19. (1 pt) Library/FortLewis/Algebra/5-6-Linear-systems/MCH1-5-622-Linear-systems.pg
is
,s=
r=
,t=
,u=
.
Correct Answers:
•
•
•
•
Find the point of intersection of the lines in the figure,
given that line A, in red, has equation y = x + 3 and line
B, in blue, has equation 2x + 3y = 12.
-6
-1
-1
-6
x=
y=
3
22. (1 pt) Library/CollegeOfIdaho/setAlgebra 03 01 SystemOfLinearEq/31IntAlg 03 LinearSystem.pg
(Click on graph to enlarge)
The graphs of two linear equations are shown above. Find
the solution.
Answer:
Correct Answers:
• -3 / -5
• -18 / -5
20.
(1
/solve RREF.pg
Correct Answers:
• None
pt)
23.
(1 pt) Library/WHFreeman/Holt linear algebra/Chaps 1-4/holt 01 04 028.pg
Library/Rochester/setAlgebra35SystemMatrices-
Find the values of the coefficients a, b and c so that the conditions
Given the augmented matrix below, solve the associated system
of equations. For your variables, use x1, x2, x3, x4, x5, and x6.
f (0) = 6,

1
 0
0
−2
0
0
The solution is (
−4
1
0
,
0 3
−3 4
0 0
,
5
−3
1
,
−1
−3 
−6
and
f 00 (0) = −3
hold for the function
f (x) = aex + be−2x + ce3x .
,
a=
b=
)c =
,
Correct Answers:
•
•
•
•
•
•
f 0 (0) = −15,

Correct Answers:
• 4
-1--2*(x2)--4*(-3--3*(x4)-4*(x5)--3*(-6))-0*(x4)-3*(x5)-5*(-6)
• 5
x2
• -3
-3--3*(x4)-4*(x5)--3*(-6)
x4
24.
(1 pt) Library/WHFreeman/Holt linear algebra/Chaps 1-4x5
/holt 01 04 022.pg
-6
When using partial fractions to find antiderivatives in calculus
we decompose complicated rational expressions into the sum
of simpler expressions that can be integrated individually. The
required decomposition is
21. (1 pt) local/Library/UI/holt 01 01 002.pg
Determine which of the points (−1, −1, 0), (−5, 1, −1), and
(2, −5, 2) lie in the plane x1 − 3x2 − 5x3 = 2.
A Bx +C
30
= + 2
x(x2 + 5)
x
x +5
Find the values of the missing constants.
A=
B=
C=
Answer:
Correct Answers:
• (-1,-1,0)
Correct Answers:
4
• 6
• -6
• 0
If a system of linear equations has an infinite number of
solutions, then its associated augmented matrix has a column
corresponding to a free variable.
A system of equations can have exactly 1 solution.
• A. True
• B. False
• A. True
• B. False
Correct Answers:
• A
• B
• A
• B
• A
A system of linear equations can have exactly 1 solution.
• A. True
• B. False
26.
(1 pt) Library/WHFreeman/Holt linear algebra/Chaps 1-4-
/2.1.7.pg
A system of linear equations has no solution if and only if
there is a pivot column in the echelon form of its augmented
matrix.
Express the following vector equation as a system of linear
equations.
4
2
−5
x1
+ x2
=
−3
6
9
(Keep the equations in order.)
x1 +
x2 =
.
x1 +
x2 =
.
• A. True
• B. False
Correct Answers:
• 4
• 2
• -5
• -3
• 6
• 9
A system of linear equations has an infinite number of solutions if and only if its associated augmented matrix has a
column corresponding to a free variable.
• A. True
• B. False
c
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