Victor Camocho
math2250fall2011-2
WeBWorK assignment number Homework 5 is due : 09/22/2011 at 11:00pm MDT.
The
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having trouble figuring out your error, you should consult the book, or ask a fellow student, one of the TA’s or your professor for
help. Don’t spend a lot of time guessing – it’s not very efficient or effective.
Give 4 or 5 significant digits for (floating point) numerical answers. For most problems when entering numerical answers,
you can if you wish enter elementary expressions such as 2 ∧ 3 instead of 8, sin(3 ∗ pi/2)instead of -1, e ∧ (ln(2)) instead of 2,
(2 + tan(3)) ∗ (4 − sin(5)) ∧ 6 − 7/8 instead of 27620.3413, etc. Here’s the list of the functions which WeBWorK understands.
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1. (1 pt) Library/maCalcDB/setLinearAlgebra1Systems/ur la 1 5.pg
Solve the system using elimination

 2x+3y−3z= 35
3x−2y+4z=−14

−4x+5y−4z= 25
5. (1 pt) Library/Rochester/setLinearAlgebra1Systems/ur la 1 20.pg
Solve the system

+4x5 −5x6 = 0
 x1 +3x2 +2x3
−x4 −5x5 −5x6 = 8

x1 +3x2
+6x5 −9x6 =−4








x1






 x2 














 x3 
 +
 s +
 t
 =







 x4 














 x5 
x6


x=
y=
z=
2. (1 pt) Library/maCalcDB/setLinearAlgebra1Systems/ur la 1 7.pg
Write the augmented matrix of the system

x−69y−21z= 11

−77y +6z=−2

−91x
+34z=−2






+






 u.




6. (1 pt) Library/Rochester/setLinearAlgebra1Systems/ur la 1 6.pg
3. (1 pt) Library/Rochester/setLinearAlgebra1Systems/ur la 1 13.pg
Solve the system
4x1 +x2 = 7
8x1 +2x2 =14
x1
+
s.
=
x2
For each system, determine whether it has a unique solution
(in this case, find the solution), infinitely many solutions, or no
solutions.
1.
−5x−8y=−6
4x−7y= 45
• A. No solutions
• B. Unique solution: x = −3, y = 6
• C. Unique solution: x = 0, y = 0
• D. Unique solution: x = 6, y = −3
• E. Infinitely many solutions
• F. None of the above
2.
−2x +4y=18
−6x+12y=54
• A. Infinitely many solutions
4. (1 pt) Library/Rochester/setLinearAlgebra1Systems/ur la 1 19.pg
Solve the system

5x1 −6x2 +4x3 +4x4 = 2



−x1 +x2 +3x3 +3x4 = 4
4x1 −5x2 +7x3 +7x4 = 6



3x1 −3x2 −9x3 −9x4 =−12
 




 
x1
 



 x2  
 +
 s +
 t.

 
 



 x3  =
x4
1
•
•
•
•
•
B. Unique solution: x = 0, y = 0
C. No solutions
D. Unique solution: x = 18, y = 54
E. Unique solution: x = −9, y = 0
F. None of the above
3.
4.
6x+2y=0
5x+5y=0
A. Unique solution: x = 0, y = 0
B. Unique solution: x = −5, y = 6
C. Infinitely many solutions
D. Unique solution: x = 8, y = 10
E. No solutions
F. None of the above
•
•
•
•
A. Infinitely many solutions
B. No solutions
C. Unique solution
D. None of the above
1 0 0
4
0 0 1 -18
•
•
•
•
A. Infinitely many solutions
B. Unique solution
C. No solutions
D. None of the above
0 1 0 -6
0 0 1 7
•
•
•
•
A. No solutions
B. Infinitely many solutions
C. Unique solution
D. None of the above
3.
4.
•
•
•
•
•
•
1
0
2.
•
•
•
•
•
•
5x +6y= 8
−15x−18y=−23
A. No solutions
B. Unique solution: x = −23, y = 8
C. Unique solution: x = 0, y = 0
D. Unique solution: x = 8, y = −23
E. Infinitely many solutions
F. None of the above
0
1
3
-17
10. (1 pt) hw5/p11.pg

-2 -1
0 -4 3
If A = 2 4 -4  and B = -1 -3
0 0
2 -3 -2

7. (1 pt) Library/Rochester/setLinearAlgebra1Systems/ur la 1 8.pg
Determine the value of h such that the matrix is the augmented
matrix of a consistent linear system.
3 −2 h
−9
6 3
Then 3A − 2B =

4
0 
2

h=
11. (1 pt) Library/Rochester/setLinearAlgebra2SystemsApplications/ur la 2 2.pg
8. (1 pt) Library/Rochester/setLinearAlgebra1Systems/ur la 1 18.pg
Solve the system

x1 +x2
=−5



x2 +x3
=−5
x
+x

3
4 =−5


x1
+x4 =−5
 


 
x1
 

 x2  
 +
 s.

 
 

 x3  =
x4
Find the quadratic polynomial whose graph goes through the
points (−2, 4), (0, 4), and (1, 10).
f (x) =
x2 +
x+
12. (1 pt) Library/TCNJ/TCNJ LinearSystems/problem16.pg
Determine whether the following systems have no solution, an
infinite number of solutions or a unique solution.
9. (1 pt) Library/Rochester/setLinearAlgebra1Systems/ur la 1 22.pg
The reduced row-echelon forms of the augmented matrices of
four systems are given below. How many solutions does each
system
 have?

1 0 14 0
1.  0 1 2 0 
0 0 0 1
• A. No solutions
• B. Unique solution
• C. Infinitely many solutions
• D. None of the above
? 1.
? 2.
? 3.
2
−x
−6 x
−13 x
−x
−6 x
−13 x
25 x
−10 x
−35 x
−
+
+
−
+
+
−
+
+
y
5y
9y
y
5y
9y
20 y
8y
28 y
=
=
=
=
=
=
=
=
=
1
9
19
1
9
18
−5
2
7
2x
−3x
2x
? 2.
−3x
2x
? 3.
−5x
? 1.
13. (1 pt) Library/TCNJ/TCNJ LinearSystems/problem10.pg
Give a geometric description of the following system of equations.
c
Generated by the WeBWorK system WeBWorK
Team, Department of Mathematics, University of Rochester
3
−
+
−
+
−
+
4y
6y
4y
6y
4y
3y
=
=
=
=
=
=
12
−18
12
−15
12
10