Recent content by jclawson709

ok so yeah, a basis is a set of vectors that are linearly independent. so if {f_0,...,f_n} is a basis then a_0f_0 + a_1f_1 + ... + a_nf_n = 0 if and only if a_0, a_1, ..., a_n are all zero, right?

Homework Statement Let V = P_n(F), and let c_0, c_1,..., c_n be distinct scalars in F. For 0 <= i <= n, define f_i(p(x)) = p(c_i). Prove that {f_0, f_1,..., f_n} is a basis for V*. Hint: Apply any linear combination of this set that equals the zero transformation to p(x) =...

Hmm no I just presumed intuitively that that was the answer, i didn't think it all the way out like that. So for part b, would I write W1 = (0,s), W2 = (s,0) so W1 + W2 = (s,s) and therefore T(x) = (0,s)?

oops i actually meant T(a,b) = (0,b) for part a

Homework Statement Let T: R^2 -> R^2. Part a: Find a formula for T(a,b) where T represents the projection on the y-axis along the x-axis. Part b: Find a formula for T(a,b) where T represents the projection on the y-axis along the line L={(s,s):s is an element of R} Homework...