Question

LINEAR ALGEBRA

1. (4 marks) Show that the set of vectors {ū = (1,1,1,1), űz = (1,0, -1,0), vz = (0,1,0, -1)} is orthogonal. Use those vectors in the set to get an orthonormal set {w1, W2, W3}.

Answer 1

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Hope this helps you! Thank you {1,2, in is said to be orthogonal is vi - Vj = 0 it i wow, J. =1,2,.n 3=1,2, .. {yu, .- Vi is said to be orthonormal its vi Vj = 0 sriti and Vi=1 sri- らj=1;2-n. Griven that, I = (1, 1, 1, 1), B = (1,0, 1, 0) 33 = (0,1,0,-1) = 1.1+10+1(4) + 10 =1-1=0 V2 V3 = 1.0 +0.1 +(-1.0+ 0.6-1) = 0 3. 3 = 1.0+1.1+1.0t 1(-1) = 12120 sou, 2 is orthogonal. Now, w, (1,1,1,1) lluill W, - vo - (1,0,1,0) = (0,0) w (°), ) = ( ) 3) TV w. w 1, wewe = 1, wo w = 1 and we. Wy = 0 sor its , 1 = 1,2,3. so, & w, we we} is orthonormal. Sittit 2 Then