Question

If the matrix $\begin{bmatrix} 0 & 2\beta & \gamma \\ \alpha & \beta & - \gamma \\ \alpha & - \beta & \gamma \end{bmatrix}$ is orthogonal, then

• A. a = ±$\frac{1}{\sqrt{2}}$
• B. b = ± $\frac{1}{\sqrt{6}}$
• C. g = ± $\frac{1}{\sqrt{3}}$
• D. All of these

Answer 1

Answer: (D)

All of these

Answer 2

since A is orthogonal,

AA´ = I

$\begin{bmatrix} 4\beta^{2} + \gamma^{2} & 2\beta^{2} - \gamma^{2} & - 2\beta^{2} + \gamma^{2} \ 2\beta^{2} - \gamma^{2} & \alpha^{2} + \beta^{2} + \gamma^{2} & \alpha^{2} - \beta^{2} - \gamma^{2} \

• 2\beta^{2} + \gamma^{2} & \alpha^{2} - \beta^{2} - \gamma^{2} & \alpha^{2} + \beta^{2} + \gamma^{2} \end{bmatrix}$=$\begin{bmatrix} 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{bmatrix}$

\ a = ± $\frac{1}{\sqrt{2}}$, b = ± $\frac{1}{\sqrt{6}}$, g = ± $\frac{1}{\sqrt{3}}$