(4) Let f : R' - R' be defined by f(x, y) := (2 - x + 3y + y',3x - 2y - ry) Use directly the definition of the derivative to show that f is differentiable at the origin and compute f'(0, 0). Hint: If the derivative exists, it is in L(R', R?), so it can be represented by a 2x2 matrix.(2) Fix an interval [a, b]. Let Cla, b] be the set of continuous functions from [a, b] to R. For f. g E Cfa, b], define a dot product and norm by 1/2 f . 9 := [ f(ajg(r) dr, = (note the absolute value is actually not necessary). The dot product is clearly bilinear and symmetric (you do not need to show this or that . defines a dot product). Show that . 2 is a norm on Ca, b]. domain