Given x1 = (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, and 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.
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