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Statement of a problem № m467

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A function f: Rn x Rm-> Rp is bilinear if for x,x1, x2 € R n, y,y1, y2 € Rm and a € R We have, f(ax, y) = af (x, y) = f(x, ay) f(x1 + x2, y) = f(x1, y) + f(x2, y) f(x, y1 +y2) = f(x, y1) + f(x, y2) (a) Prove that if f is bilinear, then (b) Prove that Df (a, b) (x, y) = f (a,y) + f(x,b). (c) (Show that the formula for Dp (a, b) in theorem 2-3 is a special case of (b




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