i have to do a lin. algebra induction proof, and i'm not sure how to go about it. here it is:
let x1,....xn+1 (that means x sub 1 through x sub n+1...sorry, i dont know how to do subscripts on this thing) be vectors in the set of real numbers.
(a) show that there exist real numbers a1,....an+1, not all zero, such that the linear combination a1x1 +....+an+1 xn+1 = 0.
(b) using part a, show that
xi (again, meaning x sub i) = b1x1 +....+bi-1 xi-1 +...+bn+1 xn+1, for some i, 1 is less than or equal to i, which is less than or equal to n+1, and some b1,...bi-1, bi+1,...bn+1 is in the set of real numbers.