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 - 11d W= d : c, d real c - 11d Let w = d . Then w is an element of W. Write w in parametric vector form. w = c + d (c, d in R) 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 of an m xn matrix A is a subspace of RM. 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