Q. Let x1 = (2, 1, 3)T , x2 = (3, 1, 4)T , x3 = (2, 6, 4)T ,

(a) Is {x1, x2, x3} a basis for R 3 ?

(b) Does {x1, x2} span R 3 ? What is the dimension of Span({x1, x2})?

(c) What other vector can we add to {x1, x2} to make it into a basis?

(d)Prove that if v1, v2, . . . , vn form a basis of R^n and A is a invertible matrix, then Av1, Av2, . . . , Avn is also a basis for R^n .