(3) Consider the following vectors in R*: VI= Answer the following questions; you must justify your answer. (a) Are vi, V2, Va linearly independent? (b) Do v1, V2 Vi, w span R'? (c) Is w in the span of v1, v2, va? If yes, write w as a linear com- bination of v1, v2, va; if no, explain why not. (4) Find the determinant and inverse of the matrix 3 -5 8 6 (5) Suppose that A is a 2 x 2 matrix such that det A = 3, and let B be the 2 x 2 matrix obtained from the identity matrix / by first adding 3 times its first row to its second row, then scaling its first row by 2. Let C = 24 B ' and let D = A + B-1. You now have enough information to compute exactly one of det C and det D. Identify which one it is and compute it. (6) Let S be the parallelepiped determined by 3 vectors and Let 7 : R3 - R be the linear transformation with the associated matrix (a) Find the volume of S. (b) Find the volume of T(S). (7) For the matrix 5 0 1 -2 (a) Find a basis for the column space of A and determine its di- mension. (b) Find a basis for the null space of A and determine its dimension