(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. 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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# Homework Help: Vector Basis of R^n

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