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JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If \(P=\left[\begin{array}{ll}1 & 0 \\ 1 / 2 & 1\end{array}\right]\), then \(P^{50}\) is:
- A \(\left[\begin{array}{cc}1 & 25 \\ 0 & 1\end{array}\right]\)
- B \(\left[\begin{array}{ll}1 & 0 \\ 25 & 1\end{array}\right]\)
- C \(\left[\begin{array}{ll}1 & 0 \\ 50 & 1\end{array}\right]\)
- D \(\left[\begin{array}{cc}1 & 50 \\ 0 & 1\end{array}\right]\)
Answer & Solution
Correct Answer
(B) \(\left[\begin{array}{ll}1 & 0 \\ 25 & 1\end{array}\right]\)
Step-by-step Solution
Detailed explanation
\(P=\left[\begin{array}{cc}1 & 0 \\ \frac{1}{2} & 1\end{array}\right]\) \(P^{2}=\left[\begin{array}{ll}1 & 0 \\ \frac{1}{2} & 1\end{array}\right]\left[\begin{array}{ll}1 & 0 \\ \frac{1}{2} & 1\end{array}\right]=\left[\begin{array}{ll}1 & 0 \\ 1 & 1\end{array}\right]\)…
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