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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.

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hint: $A$ is orthogonal iff $A\cdot A^{T} = I$. You can work out the equations.

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  • $\begingroup$ Is this how it should be solved? Why did you get a negative review?? :( $\endgroup$ – marg_ocruz Mar 31 '15 at 3:53
  • $\begingroup$ alright. thanks! :) $\endgroup$ – marg_ocruz Mar 31 '15 at 4:04
  • $\begingroup$ is it not $A^T \cdot A = I$? $\endgroup$ – marg_ocruz Mar 31 '15 at 4:36
  • $\begingroup$ Both are true. You might just use one of them. $\endgroup$ – DeepSea Mar 31 '15 at 4:39
  • $\begingroup$ I see they're just the same.. :) okay! $\endgroup$ – marg_ocruz Mar 31 '15 at 4:39

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