Question
) Are there values of for which the matrix
Answer :
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We are asked to find values of (a \in \mathbb{C}) for which the matrix [ A = \begin{bmatrix} 1 & 0 & 0 \ 0 & -\frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} \ 0 & \frac{1}{\sqrt{2}} & a \end{bmatrix} ] has certain properties (implicitly, typically invertible, singular, or eigenvalues real, etc.—since not explicitly stated, the usual interpretation is to find values of (a) that make the matrix singular, i.e., (\det(A)=0)).
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