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Question: Answered & Verified by Expert
Let M=0-αα0, where α is a non-zero real number and N=k=149M2k. If I-M2N=-2I, then the positive integral value of α is ______.
MathematicsMatricesJEE MainJEE Main 2022 (29 Jun Shift 2)
Solution:
1599 Upvotes Verified Answer
The correct answer is: 1

Given, M=0-αα0

Now, M2=-α200-α2=-α2I

Also given, N=k=149M2k

N=M2+M4+.+M98=-α2+α4-α6+..I

=-α21--α2491+α2.I

N1+α2=-α2α98+1

NI-M2=-α2α98+1

Now comparing with I-M2N=-2I

We get, α=1.

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