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zairizain
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Homework Statement
Let V=(x1,x2,..Xn) Sum X = 0 be a subspace of R^n. Find a basis of V such that Sum X^2=1
Homework Equations
The Attempt at a Solution
for Sum X =0
x1+x2+..+xn =0
xn= -x1-x2-...
So <x1, x2, ...,-x1-x2-...>=<x1, 0,0...,-x1> +<0,x2,0,...,-x2)+...
=x1<1,0,0,...,-1>+x2<0,1,0,...-1>+...
norm, ||x1||=||x2||=||xn||=... = 2^(1/2)
Basis {<1/norm x1, 0, 0,..-1/norm x1>, <0,1/normx2,0,...-1/normx2>,...}For Sum X^2=0
x1^2 +x2^2+...+xn^2 =1
xn^2 = 1- (x1^2 +x2^2+...)
That all I can do. Please guide me.
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