1. Mehmet Emin YA?AR MATH201 SU2014
WeBWorK assignment number math201 su2014 hw1 is due : 07/20/2014 at 05:35pm EDT.
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1. (1 pt) Solve the system using elimination
2x+4y−3z= 31
−5x−6y−4z=−12
−3x−5y−2z=−12
x =
y =
z =
2. (1 pt) Solve the system using elimination
4x+9y=25
5x−3y=17
x =
y =
3. (1 pt) Write the augmented matrix of the system
18x +51z=−4
3x +3y −z= 4
82x+69y = 6
4. (1 pt) Find a and b such that
-7
-12
-7
= a
1
4
2
+b
2
-8
-3
.
a =
b =
5. (1 pt) If A =
x 2
y -6
, determine the values of x and y
for which A2 = A.
x = ,
y = .
6. (1 pt) −4x+1y+6z = −9
1x+3y−6z = 9
8x+1y+5z = 5
Write the above system of equations in matrix form:
∗
x
y
z
=
7. (1 pt) If A =
-3 0 -1
-2 -1 -2
-1 -2 -2
and B =
-2 -2 4
0 3 3
3 3 4
Then 2A+B =
and AT =
8. (1 pt) Given the matrices
B =
2 -2 -1
1 3 -2
, C =
0 1 -5
4 -4 5
,
find C −B. Write C −B as
C −B =
a11 a12 a13
a21 a22 a23
.
Input your answer below:
a11 =
a12 =
a13 =
a21 =
a22 =
a23 =
1
2. 9. (1 pt) If A =
-4 3 -2
3 -4 0
4 -4 2
and B =
-4 2 2
-4 3 -3
0 -3 0
Then 3A−3B =
and 2AT =
10. (1 pt) Solve the system using matrices (row operations)
−2x−5y+3z=−38
−3x−6y+6z=−51
−2x+3y+4z= 1
x =
y =
z =
11. (1 pt) Solve the system
x1+x2 = 2
x2+x3 = 3
x3+x4=−5
x1 +x4=−6
x1
x2
x3
x4
=
+
s.
12. (1 pt) Solve the system
x +y=−9
2x−5y= 52
6x−8y= 86
x =
y =
13. (1 pt) Solve the system
x1 +x2+3x3=−9
4x1+5x2+3x3= 1
x1
x2
x3
=
+
s.
14. (1 pt) Solve the system
x1 +4x3 +4x4= −37
x2 −2x3 −2x4= 15
3x1−2x2+17x3+16x4=−147
−x2 +2x3 +7x4= −30
x1 =
x2 =
x3 =
x4 =
15. (1 pt) Solve the system
4x1−3x2+4x3+3x4 =1
−x1 +x2+3x3+3x4 =1
3x1−2x2+7x3+6x4 =2
−2x1+2x2+6x3+6x4 =2
x1
x2
x3
x4
=
+
s +
t.
16. (1 pt) Solve the equation
−2x+5y−9z = −16.
x
y
z
=
+
s +
t.
17. (1 pt) Solve the system
x1−3x2+2x3 −3x5−4x6=−5
−x4+5x5−4x6=−3
x1−3x2 +5x5−6x6=−1
x1
x2
x3
x4
x5
x6
=
+
s +
t
+
u.
18. (1 pt) If the following system has infinitely many solu-
tions,
−5x − 3y + 5z = 5
−4x + 4y − 3z = −4
−23x − y + hz = k
then k = , h =
19. (1 pt) Determine all values of h and k for which the
system
5x − 6y − 7z = −4
−2x + 2y − 4z = 5
x − 2y + hz = k
has no solution.
k =
h =
2
3. 20. (1 pt) Suppose h,k are unknown constants. If the follow-
ing system of equations has a unique solution,
7x − 4y + 5z = 3
3x − 3y + 7z = −3
−13x + 10y + hz = k
then h = A, where A = .
Now suppose that we let h = A. For how many values of k
will the above system have a solution? Type ”none” for no val-
ues, ”unique” for a unique value of k, or ”infinite” for infinitely
many values.
k =
21. (1 pt) Write a vector equation
x+
y+
z =
that is equivalent to the system of equations:
4x + 3y + 7z = −4
9x − 7y + 4z = 8
x − y − 4z = −9
22. (1 pt)
To see if b =
2
-19
12
is a linear combination of the vectors
a1 =
4
3
-3
and a2 =
-10
9
10
one can solve the matrix equation Ax = c where the columns of
A are
v1 =
and v2 =
and c =
.
23. (1 pt) Determine the value of k for which the system
x +y+2z= 3
x +2y−4z= 3
7x+17y+kz=22
has no solutions.
k =
24. (1 pt)
The system
−4x − 12y − 29z = 0
6x + 19y + 46z = 0
2x + 6y + 14z = 0
has the solution x = , y = , z = .
25. (1 pt) Determine all values of h and k for which the
system
7x + 6y = h
−4x + ky = −2
has no solution.
k =
h =
26. (1 pt) Let A =
1 -5 4 -2 1 5
0 0 1 4 0 5
0 0 0 0 1 -4
0 0 0 0 0 0
.
Describe all solutions of Ax = 0.
x = x2
+x4
+x6
27. (1 pt) Let A =
1 -2 -2 -4
3 -6 -6 -12
.
Describe all solutions of Ax = 0.
x = x2
+x3
+x4
Generated by the WeBWorK system c WeBWorK Team, Department of Mathematics, University of Rochester
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