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...

Extracted 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.