Answer to Question #23678 in Linear Algebra for Jacob Milne

Question

Prove that the following are equivalent:

a) The set U = {u^1, u^2,..., u^n} is linearly independent;
b) u^1 does not equal 0 and no u^n is a linear combination of the members of U that precede it in the list;
c) no u^n is a linear combination of the other members of U.