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JEE Main 2005
Exam
JEE Main
Year
2005
Subject
Mathematics
Chapter
Mathematical Induction

JEE Main 2005 · Mathematics · Mathematical Induction

If A=[ array ll 1 & 0 1 & 1 array ] and I=[ array ll 1 & 0 0 & 1...

If A=\left[1011\begin{array}{ll}1 & 0 \\ 1 & 1\end{array}\right] andI=\left[1001\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right],thenwhichoneofthefollowingholdsforall, then which one of the following holds for alln \geq 1$, by the principle of mathematical indunction

Options

  1. AAn=nA−(n−1)IA^n=n A-(n-1) I
  2. BAn=2n−1A−(n−1)IA^n=2^{n-1} A-(n-1) I
  3. CAn=nA+(n−1)IA^n=n A+(n-1) I
  4. DAn=2n−1A+(n−1)IA^n=2^{n-1} A+(n-1) I

Correct answer

A. An=nA−(n−1)IA^n=n A-(n-1) I

Step-by-step solution

By the principle of mathematical induction (A) is true.
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