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- 22d :C, d real c- 22d Let w= d| Then w is an element of W. Write w in parametric vector form. (c, d in R) %3D Now write the expression found for w in the previous step as the product of a matrix, A, and the vector {}- Therefore, the set W= The

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.2: Linear Independence, Basis, And Dimension
Problem 33EQ
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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.
C-22d
W =
:C, d real
c- 22d
Let w =
Then w is an element of W. Write w in parametric vector form.
(c, d in R)
w =.
+.
Now write the expression found for w in the previous step as the product of a matrix, A, and the vector
w = A
w =
Therefore, the set W =
The
<n matrix A is a subspace of Rm.
Nul A.
The proof is complete s
Col A.
space of
- The given set W must be a vector space because a subspace itself is a vector space.
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. C-22d W = :C, d real c- 22d Let w = Then w is an element of W. Write w in parametric vector form. (c, d in R) w =. +. Now write the expression found for w in the previous step as the product of a matrix, A, and the vector w = A w = Therefore, the set W = The <n matrix A is a subspace of Rm. Nul A. The proof is complete s Col A. space of - The given set W must be a vector space because a subspace itself is a vector space.
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