Given x,=(1, 1, 1)T and x2 = (3, - 1, 4)T:
(a) Do x1 and x2 span R3? Explain.
(b) Let x3 be a third vector in R3 and set X = (x1, x2, x3). What condition(s) would X have to satisfy in order for x1, x2, x3 to form a basis for R3?
(c) Find a third vector x3 that will extend the set {x1, x2} to a basis for R3.