1. For each of the following sets of vectors in R³, determine whether the vectors span R³. For those sets that do not span give a vector in R3 that is not in the span. (a) {(1,2,0), (-1,0, 2), (3, 4, -2)}, (b) {(1, 1, 1), (1,-1, −1), (−1, 1, 1), (-1, -1, 1)}.

Find nonzero vectors a, b, and c in space such that a × b = a X c but b c.

12 If a. x and y are three non-zero and mutually non-parallel vectors, and the vectors b and e are given by b=x-(x-â)â and c=y-(y â)â-(y.b)b, where â and b are unit vectors along a and b respectively, show that a, b and c are mutually perpendicular.

Q3: Determine which of the following vectors are in span -2 If the vectors are in the span write them as a a linear combination of the above vectors, otherwise give a brief reason why the vector isn't in the span. (a) [1 2 8 1] (b) [2 4 -5 8] (c) [-3 7 11 11]