Question

Determine if the matrix
q= √3/3, √6/6, -√2/2
-√3/3, √6/3, 0
√3/3, √6/6, √2/2
Is othognal.

Answer 1

Matrix is orthogonal if its determinant is 1 or -1

solution:

find determinant

$det(q)=\sqrt{3}/3*(\sqrt{6}/3*\sqrt{2}/2-0*\sqrt{6}/6)-\sqrt{6}/6*(-\sqrt{3}/3*\sqrt{2}/2-0*\sqrt{3}/3)-\sqrt{2}/2*(-\sqrt{3}/3*\sqrt{6}/6-\sqrt{6}/3*\sqrt{3}/3)=1$

Answer: matrix is orthogonal.