JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(M =\left[\begin{array}{cc}0 & -\alpha \\ \alpha & 0\end{array}\right]\), where \(\alpha\) is a non-zero real number an \(N =\sum\limits_{ k =1}^{49} M ^{2 k }\). If \(\left( I - M ^{2}\right) N =-2 I\), then the positive integral value of \(\alpha\) is
- A \(4\)
- B \(3\)
- C \(2\)
- D \(1\)
Answer & Solution
Correct Answer
(D) \(1\)
Step-by-step Solution
Detailed explanation
\(M =\left[\begin{array}{cc}0 & -\alpha \\ \alpha & 0\end{array}\right] ; M ^{2}=\left[\begin{array}{cc}-\alpha^{2} & 0 \\ 0 & -\alpha^{2}\end{array}\right]=-\alpha^{2} I\) \(N = M ^{2}+ M ^{4}+\ldots \ldots+ M ^{98}=\left[-\alpha^{2}+\alpha^{4}-\alpha^{6}+\ldots .\right] I\)…
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