For the following exercises, use the matrices below to perform the indicated operation if possible. if not possible, explain why the operation cannot be performed. (Hint: A 2 = A ⋅ A ) A = [ − 10 20 5 25 ] , B = [ 40 10 − 20 30 ] , C = [ − 1 0 1 0 − 1 0 ] 34. A 2
For the following exercises, use the matrices below to perform the indicated operation if possible. if not possible, explain why the operation cannot be performed. (Hint: A 2 = A ⋅ A ) A = [ − 10 20 5 25 ] , B = [ 40 10 − 20 30 ] , C = [ − 1 0 1 0 − 1 0 ] 34. A 2
For the following exercises, use the matrices below to perform the indicated operation if possible. if not possible, explain why the operation cannot be performed. (Hint:
A
2
=
A
⋅
A
)
A
=
[
−
10
20
5
25
]
,
B
=
[
40
10
−
20
30
]
,
C
=
[
−
1
0
1
0
−
1
0
]
Which of the following sets of vectors are linearly independent? (Check the boxes for linearly
independent sets.)
☐ A.
70
3
13
U
B.
6
☐ C. -8
D.
☐ E.
☐ F.
23
^
2
80
-
7
8
-
°
Assume {u1, U2, 13, 14} spans R³.
Select the best statement.
A. {U1, U2, u3} never spans R³ since it is a proper subset of a spanning set.
B. {U1, U2, u3} spans R³ unless one of the vectors is the zero vector.
C. {u1, U2, us} spans R³ unless one of the vectors is a scalar multiple of another vector in the set.
D. {U1, U2, us} always spans R³.
E. {U1, U2, u3} may, but does not have to, span R³.
F. none of the above
Let H = span {u, v}. For each of the following sets of vectors determine whether H is a line or a plane.
Select an Answer
u =
3
1.
-10
8-8
-2
,v=
5
Select an Answer
-2
u =
3
4
2.
+
9
,v=
6
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