Let S = (a) Find a basis for W. (b) What is the dimension of W? and W = Span(S).

Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors {vu,wv,uw} is linearly independent or linearly dependent.

Take this test to review the material in Chapters 4 and 5. After you are finished, check your work against the answers in the back of the book. Prove that the set of all singular 33 matrices is not a vector space.

Prove that in a given vector space V, the additive inverse of a vector is unique.

Prove that if A is similar to B and A is diagonalizable, then B is diagonalizable.

Find all subsets of the set S={(1,3,2),(4,1,1),(2,7,3),(2,1,1)} that form a basis for R3.