Either use an appropriate theorem to show that the given set, W, is a vector space, or find a specific example to the contrary. c-10d W = - (+) d : c, d real C Let w = W=C W = A W = 1 0 c-10d с d Now write the expression found for w in the previous step as the product of a matrix, A, and the vector A Then w is an element of W. Write w in parametric vector form. - 10 HI + d d q[:] 1 (c, d in R)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 46E
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Either use an appropriate theorem to show that the given set, W, is a vector space, or find a specific example to the
contrary.
W =
Let w =
W = C
W = A
W =
1
1
C
c-10d
c - 10d
d
с
d
d
+
с
C
Now write the expression found for w in the previous step as the product of a matrix, A, and the vector
: c, d real!
Then w is an element of W. Write w in parametric vector form.
- 10
1
0
(c, d in R)
с
d
Transcribed Image Text:Either use an appropriate theorem to show that the given set, W, is a vector space, or find a specific example to the contrary. W = Let w = W = C W = A W = 1 1 C c-10d c - 10d d с d d + с C Now write the expression found for w in the previous step as the product of a matrix, A, and the vector : c, d real! Then w is an element of W. Write w in parametric vector form. - 10 1 0 (c, d in R) с d
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Follow-up Questions
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Follow-up Question
Either use an appropriate theorem to show that the given set, W, is a vector space, or find a specific example to the contrary.
W =
W=C
L
W = A
C
c-10d
d
1
- 10
HI
1
0
1
W = 0
1
C
C
Now write the expression found for w in the previous step as the product of a matrix, A, and the vector
[:]
d
C
"]
- 10
1
0
: c, d real
d
(c, d in R)
Therefore, the set W =
Nul A.
Col A.
Transcribed Image Text:Either use an appropriate theorem to show that the given set, W, is a vector space, or find a specific example to the contrary. W = W=C L W = A C c-10d d 1 - 10 HI 1 0 1 W = 0 1 C C Now write the expression found for w in the previous step as the product of a matrix, A, and the vector [:] d C "] - 10 1 0 : c, d real d (c, d in R) Therefore, the set W = Nul A. Col A.
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