Answer
a. False
b. True
c. True
d. False
e. False
Work Step by Step
a. The set of vectors need to span H
b. If a set of vectors span H and are linearly independent, they form the basis for V. If they are linearly dependent, vectors can be removed one by one until the remaining vectors are all linearly independent.
c. If the set of linearly independent vectors is as large as possible, it would span the vector space.
d. The standard method does not fail to produce a spanning set for Nul A
e. The pivot columns of A produce a basis for Col A, not the pivot columns of B.
