1. Find a basis for the null space and column space of each matrix. -1 (a) A = 3 -2 2 -6 (b) A = 1 4 0 1 -2 1 3 0 (c) A = 2 6 1 1 3 N JNAWAL 2 0 -1 (d) A = 4 1 2. Determine whether the set of vectors is independent or dependent. If it is de- pendent, eliminate the (and only the) redundant vectors to find an independent subset. 3. (a) Give an example of three vectors v1, V2, v3 such that (1) the vectors are lin- early dependent, and (2) if you remove any one of them the remaining two are linearly independent. (b) Give an example of three vectors w1, w2, w3 such that (1) the vectors are lin- early dependent; (2) if you remove wj then the remaining two are linearly independent, and; (3) if you remove w2 then the remaining two are linearly dependent