PrepRung
Sign inSign up free

NDA 2020 Maths · Mathematics · Matrices · medium

If A=beginbmatrix1&2\\0&1endbmatrix, then A^15 equals

Single correct option

If A=[1201]A=\begin{bmatrix}1&2\\0&1\end{bmatrix}, then A15A^{15} equals
  1. A. [13001]\begin{bmatrix}1&30\\0&1\end{bmatrix}
  2. B. [13201]\begin{bmatrix}1&32\\0&1\end{bmatrix}
  3. C. [12015]\begin{bmatrix}1&2\\0&15\end{bmatrix}
  4. D. [11501]\begin{bmatrix}1&15\\0&1\end{bmatrix}
Show answer and solution

Answer: (A) [13001]\begin{bmatrix}1&30\\0&1\end{bmatrix}

A2=[1401]A^2=\begin{bmatrix}1&4\\0&1\end{bmatrix} and by induction An=[12n01]A^n=\begin{bmatrix}1&2n\\0&1\end{bmatrix}. So A15=[13001]A^{15}=\begin{bmatrix}1&30\\0&1\end{bmatrix}. Powering each entry separately is the common error.
Report a mistake

Original question written in the NDA 2020 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