Quiz 6 Ma 322 005 Name ______________

1. If u, v, and w are vectors in V which span V, what can you say about the dimension of V?

Solution: All you can say for sure is that the dimension of V is between 0 and 3. More information about u, v and w is needed to say more.

2. Why can a basis for a vector space contain the zero vector?

Solution. Because no set of vectors containing the 0 vector is linearly independent. The members of a basis must not only span the space but also be linearly independent.

3. Let [Maple Math] .

a) What is the rank of A?

Solution: A reduced to echelon form is [Maple Math] , and has 3 pivots. So the rank is 3.

b) Write A as a sum of r rank one matrices, where r is the rank of A.

Solution: A = [Maple Math]