SOLUTION: you have 3 vectors x1 =[1, 1, 1, 1] x2=[6, 0, 0, 2] x3=[-1, -1, 2, 4] Use the gram-Schmidt algorithm to convert the set S={x1, x2, x3} into an orthogonal set.

Algebra ->  College  -> Linear Algebra -> SOLUTION: you have 3 vectors x1 =[1, 1, 1, 1] x2=[6, 0, 0, 2] x3=[-1, -1, 2, 4] Use the gram-Schmidt algorithm to convert the set S={x1, x2, x3} into an orthogonal set.      Log On


   

Question 375891: you have 3 vectors x1 =[1, 1, 1, 1] x2=[6, 0, 0, 2] x3=[-1, -1, 2, 4]
Use the gram-Schmidt algorithm to convert the set S={x1, x2, x3} into an orthogonal set.
Answer by Jk22(389) About Me  (Show Source):
You can put this solution on YOUR website!
x1 =[1, 1, 1, 1] x2=[6, 0, 0, 2] x3=[-1, -1, 2, 4]
x1->x1/|x1|=[1, 1, 1, 1]/Sqrt(4)=1/2



x2->x2-(x2.x1)x1=[6, 0, 0, 2]-1/2*(6+2)*1/2[1,1,1,1]=[6,0,0,2]-2[1,1,1,1]
=[4,-2,-2,0]
x2->x2/|x2|=[4,-2,-2,0]/Sqrt(16+4+4)=[2,-1,-1,0]/Sqrt(6)



x3->x3-(x3.x1)x1-(x3.x2)x2=
=[-1,-1,2,4]-1/4(-1-1+2+4)[1,1,1,1]-1/6(-2+1-2)[2,-1,-1,0]
=[-1,-1,2,4]-[1,1,1,1]+1/2[2,-1,-1,0]
=[-2,-2,1,3]+1/2[2,-1,-1,0]
=[-1,-5/2,1/2,3]

x3->x3/|x3|=[-1,-5/2,1/2,3]/Sqrt(1+25/4+1/4+9)
=[-1,-5/2,1/2,3]/Sqrt(33/2)