# Finding values of a, b, c of a matrix

Find for which values of $a, b, c$ the following matrix is orthogonal

$$A= \left( {\begin{array}{ccc} \sqrt{\frac{1}{2}} & a & \frac{1}{2} \\ \sqrt{\frac{1}{2}} & b & \frac{1}{2} \\ 0 & c & \sqrt{\frac{1}{2}} \\ \end{array} } \right)$$

I was thinking of doing this: Need to find $u_1 \cdot u_2 = u_1 \cdot u_3 = u_2 \cdot u_3=0$ and that $u_4 \cdot u_4= 1$ which should form the orthogonal basis vectors but then I got stuck when I found $u_1 \cdot u_3 \neq 0$. Am I right or this is not the way to do this? Please help.

hint: $A$ is orthogonal iff $A\cdot A^{T} = I$. You can work out the equations.
• is it not $A^T \cdot A = I$? – marg_ocruz Mar 31 '15 at 4:36