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If [(0,2beta,gamma),(alpha,beta,-gamma),...

If `[(0,2beta,gamma),(alpha,beta,-gamma),(alpha,-beta,gamma)]` is orthogonal, then find the value of `2alpha^(2)+6beta^(2)+3gamma^(2).`

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To solve the problem, we need to determine the values of \( \alpha \), \( \beta \), and \( \gamma \) such that the given matrix is orthogonal. The matrix is given as: \[ A = \begin{pmatrix} 0 & 2\beta & \gamma \\ \alpha & \beta & -\gamma \\ \alpha & -\beta & \gamma \end{pmatrix} ...
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