Question

Problem #18: [2 marks] Let W be the subspace of R4 spanned by the vectors u - (1,0,1,0), u2 = (0.-1, 1.0), and ug = (0.0, 1,-1). Use the Gram-Schmidt process to transform the basis (uj, u, uz) into an orthonormal basi (A) v1 = (-12,0, 2.0), v2 - (VG VG VG, o), v3 - (I ) (B) v1 = (-V2.0, .), v2 - (VG VG VG o), v3 - (™J - V3 VI-V3) (C) v1 - ($2.0, 92.0), v2 - (_VO YO YO,), v3 - (-93. VI - VZ) (D) v1 = (-2.0.72.0), 12 - (no yo yo .o), v3 - (XIV (E) v1 = (72, 0, 92.0), v2 = (-4G YO), v3 - (-VI VI VET - Y3) (F) v1 - (2,0,43,0), 2 - (- yo yo yo), v3 - (-VI-VI VIVO (G) v1 = (V2.0, V7.0), v2 - (-vā , O), v3 - (_V3 VID) (I) v1 = (-V3.0. YZ, O), v2 = (Y6 - Yo Yo .0), v3 - (NI V VE _V3) Select Save Your work has been saved! (Back to Admin Page) Problem #19: [3 marks] Consider the following statements. (1) If A is nxn then 4'4") - 1. (11) If A is an nxn matrix, then tr(CA) = c t (.). (iii) If A? A is a symmetric matrix, then A must be a square matrix Determine which of the above statements are True (1) or False (2). So, for example, if you think that the answers, in the above order, are True False False, then you would enter 1,2,2 into the answer box below (without the quotes). Problem = 19

Answer 1

18.

answer:- (option E)

solution:

GIVEN = (1,0,1,0 ,₂ = (0,-1,1,0), B3= (0,0,1,-1) Laphull AS WE KNOW Step Tu = v In Gram - schmidth process Step-3 z = V₂ - U, V3 ru - Mr V3 lbs Us.dly a on solving honso llz=1 - 3 Step-2 - إيبات اتن " U₂ = V2 - Lepo V2 u U. 4 on solving Vų. gold lly = [- SO, Coption E -do = ll2 to go M ez (-13 43 3 - 2
19.

answer: (1,2,2)

solution:

#19 i True (1) AT (ADT AT (AT) - I (1) FALSE (2) to (CA) = nc tr(A) (ii) FALSE (2) A A is symmetric - CATAT = ATA - AT (AT)TZATA ATA = ATA - it is true for any matrix not for only Square Matrix