Victor Camocho
math2250fall2011-2
WeBWorK assignment number Homework 7 is due : 10/06/2011 at 11:00pm MDT.
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5.
1. (1 pt) Library/Rochester/setAlgebra34Matrices/determinant 2x2a.pg
If
(1 pt) Library/Rochester/setLinearAlgebra6Determinants-
/ur la 6 9.pg
A=
find |A| =
3 − 3i 1 − 2i
−2 + 4i 1 − 2i
If A and B are 4 × 4 matrices, det (A) = 2, det (B) = 6, then
det (AB) =
,
det (2A) =
,
det (AT ) =
,
,
det (B−1 ) =
det (B3 ) =
.
.
2.
(1 pt) Library/Rochester/setLinearAlgebra6Determinants/ur la 6 15.pg
6.
(1 pt) Library/Rochester/setLinearAlgebra6Determinants/ur la 6 22.pg
Find the determinant of the matrix

3 0 0 -1 0
 -1 0 1 0 0 



M =
 0 2 0 0 -1  .
 0 0 0 2 -3 
0 1 -3 0 0
.
det (M) =
3.
Suppose that a 4 × 4 matrix A with rows v1 , v2 , v3 , and v4 has
determinant
 det A = 5. Find the following determinants:

6v1
 v2 

det
,
 v3  =
v
 4
v2
 v3 

det
,
 v4  =
v
 1

v1


v2

det
.
 v3 + 5v4  =
v4
(1 pt) Library/Rochester/setLinearAlgebra6Determinants-
/ur la 6 6.pg
Determine
allminors and cofactors of
5 5
A=
.
-7 9
M11 =
, C11 =
,
M12 =
, C12 =
,
, C21 =
,
M21 =
M22 =
, C22 =
.
7. (1pt) Library/TCNJ/TCNJ
PropertiesDeterminants/problem9.pg

1 0 1
If B = 2 1 1 
2 -1 -2
then det (B5 ) =
4. (1pt) Library/TCNJ/TCNJ
MatrixInverse/problem13.pg

4 -3 4 6
 0 5 3 1 

If A =
 0 0 2 1 
0 0 0 1


Then A−1 =

8.
(1 pt) Library/Rochester/setLinearAlgebra8VectorSpaces/ur la 8 10.pg



3
3
.
and y =
-2
4
Find the vector v = 3x − 5y and its additive inverse.
Let x =
1
v=
,
−v =
14.
,
9.
-11
Express the vector v =
as a linear combination of
2
-4
-5
x=
and y =
.
1
2
v=
x+
y.
(1 pt) Library/Rochester/setLinearAlgebra8VectorSpaces-
/ur la 8 9.pg
Let u = (0, 6, −2) and v = (−6, −1, 2).
Find the vector w = 5u − 2v and its additive inverse.
w=(
,
,
),
−w = (
,
,
),
10.
15.





-8
-52
-4
Let A = -5  , B = -28  , and C = -1  .
47
4
7
(1 pt) Library/Rochester/setLinearAlgebra8VectorSpaces-
Which of the following sets are subspaces of R3 ?
? 1. Determine whether or not the three vectors listed above
are linearly independent or linearly dependent.
A. {(x, y, z) | 3x + 8y − 6z = 0}
B. {(3, y, z) | y, z arbitrary numbers }
C. {(x, y, z) | x + y + z = −7}
D. {(x, y, z) | x, y, z > 0}
E. {(7x, 2x, 4x) | x arbitrary number }
F. {(x, 0, 0) | x arbitrary number }
If they are linearly dependent, determine a non-trivial linear
relation - (a non-trivial relation is three numbers which are not
all three zero.) otherwise, if the vectors are linearly independent, enter 0’s for the coefficients, since that relationship always
holds.
A+
B+
C = 0.
11. (1pt) Library/TCNJ/TCNJ


VectorSpaces/problem5.pg


 
-5
-10
-36
5
Let v1 = 4  , v2 = 7  , v3 = 26  and w = 6 
5
10
35
8
.
1. Is w in {v1 , v2 , v3 }? Type ”yes” or ”no”.
You can use this row reduction tool to help with the calculations.
16.





-2
-6
-14
Let v1 = 2  , v2 = 5  , and y = 12  .
-4
-15
h
For what value of h is y in the plane spanned by v1 and v2 ?
h=
3. How many vectors are in Span {v1 , v2 , v3 }? Enter ”inf” if
the answer is infinitely many.
17.
4. Is w in the subspace spanned by {v1 , v2 , v3 }? Type ”yes”
or ”no”.
12. (1 pt) Library/TCNJ/TCNJ VectorSpaces/problem4.pg


-5s-2t
 -3s-t 

Let W be the set of all vectors of the form: 
 -5s+t  . Find
-4s-4t
vectors
 u andv suchthat W =Span {u, v}.
13.


 , v =


(1 pt) Library/Rochester/setLinearAlgebra9Dependence-
/ur la 9 8.pg

2. How many vectors are in {v1 , v2 , v3 }? Enter ”inf” if the
answer is infinitely many.

u =

(1 pt) Library/Rochester/setLinearAlgebra9Dependence-
/ur la 9 1.pg

/ur la 8 6.pg
•
•
•
•
•
•
(1 pt) Library/Rochester/setLinearAlgebra9Dependence-
/ur la 9 10.pg
(1 pt) Library/Rochester/setLinearAlgebra9Dependence-
/ur la 9 11.pg
Find a linearly
3
subspace

 of
R
-1
-5
 -3  ,  -3
-2
-4
independent set of vectors that spans the same
as
by the vectors
 that
 spanned

2
, 0 .
1
 


Linearly independent set: 



,
.
18. (1 pt) Library/TCNJ/TCNJ MatrixEquations/problem8.pg
Do the columns of the matrix span R2 ?
(1 pt) Library/Rochester/setLinearAlgebra9Dependence-
/ur la 9 7.pg
? 1. A =
? 2. A =
? 3. A =
Thevectors



 
-3
4
2
v = -8  , u = 12  , and w = 4  .
-5
-5 +k
2
are linearly independent if and only if k 6=
.
2
8
1
-3
-9
9
-5
-32
-4
-15 -60
-45 -180
6
7
-7
? 4. A =
-1
-39
-12
6
3

? 2. 
19. (1 pt) Library/TCNJ/TCNJ MatrixEquations/problem13.pg
Do the following sets of vectors span R3 ?

? 3. 


 
 

1
-5
-2
? 1.  -1  ,  7  ,  5 
-3
7
1
? 4. 
c
Generated by the WeBWorK system WeBWorK
Team, Department of Mathematics, University of Rochester
3
3
3
-1
1
1
-2
-3
1
-2
 
,
 
,
 
,
-6
-6
3
-4
-4
7
12
-4
9
 

-12
 ,  -12 
5
 
 

7
-11
 ,  7  ,  -11 
-12
19

