Let B = {1; cos t; cos 2t; cos 3t; cos 4t} and C = {1; cos t; cos²t; cos³t; cos⁴t}

(iii) List the C-coordinate vectors of the elements of B, then show that the ele-

ments of B are linearly independent by showing that their C-coordinate vectors

are linearly independent.

Since the span of C has dimension 5, by the Basis Theorem we see that the

elements of B form a basis for the span of C.