Let S = {$\displaystyle v_1, v_2,....v_k$} be an orthogonal set of vectors in $\displaystyle R^n$. If S is linearly dependent, prove that one of the $\displaystyle v_j$ must be the zero vector.

Find an orthonormal basis for the column space of the matrix A =

[2 5 7]

[3 1 8]

[6 6 10]

[0 6 -9] and obtain the QR factorisation of A.