PrepRung
Sign inSign up free

NDA 2017 Maths · Mathematics · Matrices · medium

If A=beginpmatrix1&2\\0&1endpmatrix, the top-right entry of A^10 is

Single correct option

If A=(1201)A=\begin{pmatrix}1&2\\0&1\end{pmatrix}, the top-right entry of A10A^{10} is
  1. A. 2020
  2. B. 1010
  3. C. 10241024
  4. D. 2102^{10}
Show answer and solution

Answer: (A) 2020

A2=(1401)A^2=\begin{pmatrix}1&4\\0&1\end{pmatrix} and by induction An=(12n01)A^n=\begin{pmatrix}1&2n\\0&1\end{pmatrix}. So the entry is 20. Raising each entry to the power 10 is not valid for matrices.
Report a mistake

Original question written in the NDA 2017 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake