Let F: R Rm and G: Rm RP be mappings. Prove that (GF) *...

Transcribed Image Text:

Let F: R → Rm and G: Rm → RP be mappings. Prove that (GF) * = G*F*. = 3, m = p = 2. It might Use matrix multiplication to do this problem. If you want you may use n = be helpful to use x = (x1,...,xn) as coordinates for R" and y = (y₁, ..., ym) as coordinates for Rm. It may also help to introduce the notations F(x) = (f1₁(x),..., fm (x)) and G(y) = (91(y),..., 9p (y)) and the intermediate function H = GoF with H(x) = (h₁(x),..., hp(x)) = (9₁(F(x)),..., 9p(F(x))) = (91(f1 (₁,...,n),..., fm (1,...,xn)),..., 9p (f1 (1, ..., n),..., fm (1, ..., In))). Let F: R → Rm and G: Rm → RP be mappings. Prove that (GF) * = G*F*. = 3, m = p = 2. It might Use matrix multiplication to do this problem. If you want you may use n = be helpful to use x = (x1,...,xn) as coordinates for R" and y = (y₁, ..., ym) as coordinates for Rm. It may also help to introduce the notations F(x) = (f1₁(x),..., fm (x)) and G(y) = (91(y),..., 9p (y)) and the intermediate function H = GoF with H(x) = (h₁(x),..., hp(x)) = (9₁(F(x)),..., 9p(F(x))) = (91(f1 (₁,...,n),..., fm (1,...,xn)),..., 9p (f1 (1, ..., n),..., fm (1, ..., In))).