Question

By justifying your answer, determine whether the function 〈,〉〈,〉 defines an inner product on VV.

(a) 〈(u1,u2,u3,u4),(v1,v2,v3,v4)〉=u1v4−5u2v3〈(u1,u2,u3,u4),(v1,v2,v3,v4)〉=u1v4−5u2v3 and V=R4V=R4.

(b) 〈(u1,u2),(v1,v2)〉=2–√u1v1+u2v2〈(u1,u2),(v1,v2)〉=2u1v1+u2v2 and V=R2V=R2.

Answer 1

② v=1R define inher pred os. by < (46, 42, 43, 44), (44, 42, 43, 9) = 41-54g lz take e=(4, 4, 43, 4) =(5,1,1,1) to 5X11 = {u, u) = 5x1- Lu, uzzo but e to Hence, inner product does not defines an Oh IR. (6) Vaiko 2(4,4₂ ) 3 (1) 42)) = 244 + 4 U2 2(4,14), (4,4)) = 24² + 0. 24,42), (1, 28) = 241 44+ 4 ₂ 2 = 26, 4 + 42 4₂ L (4,42), (4,47 of に & (4, 4₂)+(2,42), (W, W2) = (wither, U2tl2), 1w, ws> 2 (4+) (wi) + (42+42) W2 = 24, 6, +4₂ W2) + 24 W,t U₂ W2 = 2(4,42), (W, W2)) + (11,42), 140, 102) 2 & {K (4, U2) (1, 2)) = {(ka, K42), (2, 2)) = 26 44, + Kelle = K L ( 41,42), (4,142) innerproduct on 18² AS-108 <i> de feeling