Let v1,..., vn be a basis for Rn. (a) Show that any affine function F[x] = Ax
Question:
(a) Show that any affine function F[x] = Ax + b on Rn is uniquely determined by the n + 1 vectors w0 = F[0], w1 = F[v1],..., wn = F[vn].
(b) Find the formula for A and b when v1 = e1,..., vn = en are the standard basis vectors.
(c) Find the formula for A. b for a general basis v1,..., vn.
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a First b w 0 F0 while Av i Fv i b w i w 0 for i 1 n T...View the full answer
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