Question

Answer ALL questions. (Jawab SEMUA soalan) Question 1 (10 marks] Soalan 1 [10 markah] 1B) = 3i (6) and C) = -1 1 0-31 Let A = 3 5 0 31 0 -2 questions Answer the following a) Find A B) and AIC). [2 marks] b) Determine the Hermitian conjugate for|B) and C). [2 marks] c) Compute (BIC) and (C|B). What is the relation between them? [3 marks] d) Find the normalized vector for B). [2 marks] e) Show that|B) and (C) are not orthogonal. [1 mark]

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Answer 1

A = I 0-3i 2 ley 1B) = 6) 3 J Then a 3, 0 Al B) = - 31° 2 5 243; 6 tisi 0 3. 3 i 900) IH -2 16it2 Ally 1x2 tox3,-3ix- 3*2 +5x3ť tox-1 3iX2 toxi + 2 -3° -5 - 2 D- 31° 3 5 100) - 2 3io b) Hear, Hermitian conjugate of  is (A* )= AT IBYT (2 +31 -1) and LIBYT)* = (2-37 -1) [BT - ( 2 -3; -1) Symderily (10>)+ - CO -11) (C) <BIC) = (2-4+31)-1) 1.9 = 1240 -3ix - -1) = 3 - 1 ce1B2= (0-10) ( 24373 23:) 1 (0x2+/-1 X 31 ) +(18-1) ) =-1-31 (d) <BIBY=[1] is condition of Normalited. <B1B) = ( 2-3,-1)/2 = [4 +9 +1] = 14 Thus, IB7 = 1 v 3i 2 ce <B1C) = orthogonal if (Bley to not orthogonal 12-si E =131-1) to Also <c1B) to Menu Not orthogonal