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- #1

- Apr 13, 2013

- 3,720

"Construct an orthogonal basis of [tex] R^{3} [/tex] (in terms of Euclidean inner product) that contains the vector

[tex] \begin{pmatrix}2\\1 \\-1 \end{pmatrix} [/tex] "

What I've done so far is:

Let {(a,b,c), (k,l,m), (2,1,-1)} be the basis.

Then since the basis has to be orthogonal:

(a,b,c)*(k,l,m)=0 => a*k+b*l+c*m=0

(a,b,c)*(2,1,-1)=0 => 2a+b-c=0

(k,l,m)*(2,1,-1)=0 => 2k+l-m=0

But I have three equations and six unknown variables.

What did I do wrong??What should I do???