JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let the matrix \(A=\left[\begin{array}{lll}1 & 0 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0\end{array}\right]\) satisfy \(A^n=A^{n-2}+A^2-I\) for \(\mathrm{n} \geq 3\). Then the sum of all the elements of \(\mathrm{A}^{50}\) is :-
- A \(53\)
- B \(52\)
- C \(39\)
- D \(44\)
Answer & Solution
Correct Answer
(A) \(53\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \mathrm{A}^{50}=\mathrm{A}^{48}+\mathrm{A}^2-\mathrm{I} \\ & =\mathrm{A}^{46}+2\left(\mathrm{~A}^2-\mathrm{I}\right) \\ & =\mathrm{A}^{44}+3\left(\mathrm{~A}^2-\mathrm{I}\right) \\ & =\mathrm{A}^2+24\left(\mathrm{~A}^2-\mathrm{I}\right) \\ & =25…
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