Find a third column so that the matrix

Q= [ 1./√3 1/√14 ]
[ 1/√3 2/√14 ]
[ 1/√3 -3/√14 ]

is orthogonal. It must be a unit vector that is orthogonal to the other columns; how much freedom does this leave? Verify that the rows automatically become orthonormal at the same time.

Q&A Education