Consider the following functions:(a) f(z) = x3(1 + i) − y3(1 − i)x2 + y2, (z ̸= 0), f(0) = 0,

f (x, y, z) = x2 y3 z4 .

f A = 3 -1 ,2 1Show that A2 - 4 A + 5 I2 = 0.

(1) f (x) = x2 − 4x + 3; [1, 3](2) f (x) = x3 − x; [−1, 1](3) f (x) = x3 − 9x; [−3, 3]Solution(1) f (x) = x2 − 4x + 3; [1, 3].f (1) = 1 − 4 + 3 = 0f (3) = 9 − 12 + 3 = 0The polynomial f (x) is continuous and dierentiable on [1, 3].Therefore the hypotheses of Rolle's Theorem are satised.

F=(2y−cos(x))→i−z2e3x→j+(x2−7z)→k

If f(x,y) = 3x – y2, then f(-1, 3) = -12 12 21 -21 None of these