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GATE EC 2014 Set 1 — Question 39

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NAT+2 / -0HardDeterminantsLinear AlgebraEngineering MathematicsEigenvalues & Eigenvectors

Engineering Mathematics → Linear Algebra → Determinants

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Question

Consider the matrixJ6=[000001000010000100001000010000100000]J_6 = \begin{bmatrix} 0 & 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 \\ 1 & 0 & 0 & 0 & 0 & 0 \end{bmatrix}which is obtained by reversing the order of the columns of the identity matrix I6I_6.
Let P=I6+αJ6P = I_6 + \alpha J_6, where α\alpha is a non-negative real number. The value of α\alpha for which det⁡(P)=0\det(P) = 0 is ________.
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