Write down a basis for the solution space of the equation x - y + 2z - w = 0.
Use the Gram-Schmidt orthogonalisation procedure to nd an orthonormal basis of
the solution space. (Use the standard Euclidean inner product, or dot product.)
Firstly, to write down the a basis for the solution space, can I just choose any four vectors that satisfy the given equation?
Secondly, when I do choose any vectors ie (1,1,1,2) and (5,8,3,3) I always get really messy fractions doing the orthogonalisation. Is there any way to know which vectors to choose to make it neat?