evinda
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MHB
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Hello! I am stuck at the following exercise:
"Construct an orthogonal basis of R^{3} (in terms of Euclidean inner product) that contains the vector
\begin{pmatrix}2\\1 \\-1 \end{pmatrix} "
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?
"Construct an orthogonal basis of R^{3} (in terms of Euclidean inner product) that contains the vector
\begin{pmatrix}2\\1 \\-1 \end{pmatrix} "
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?