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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 - 18d W = c, d real,

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 - 18d W = c, d real,

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.1: Vector In R^n
Problem 61E: Illustrate properties 110 of Theorem 4.2 for u=(2,1,3,6), v=(1,4,0,1), w=(3,0,2,0), c=5, and d=2....
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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. - 18d :c, d real, W = C c- 18d Let w = Then w is an element of W. Write w in parametric vector form. + d (c, d in R) W = c Now write the expression found for w in the previous step as the product of a matrix, A, and the vector d. w = A W = Therefore, the set W = The of an mxn matrix A is a subspace of R™. The proof is complete since W is a subspace 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. - 18d :c, d real, W = C c- 18d Let w = Then w is an element of W. Write w in parametric vector form. + d (c, d in R) W = c Now write the expression found for w in the previous step as the product of a matrix, A, and the vector d. w = A W = Therefore, the set W = The of an mxn matrix A is a subspace of R™. The proof is complete since W is a subspace of The given set W must be a vector space because a subspace itself is a vector space.
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