Mathematics - Matrices Question with Solution | TestHub

Given, $A=\left[\begin{array}{ccc}1& 0& 0\\ 1& 1& 0\\ 1& 1& 1\end{array}\right]$

$\Rightarrow$$A^2=\left[\begin{array}{ccc}1& 0& 0\\ 2& 1& 0\\ 3& 2& 1\end{array}\right]; A^3=\left[\begin{array}{ccc}1& 0& 0\\ 3& 1& 0\\ 6& 3& 1\end{array}\right]$

$A^4=\left[\begin{array}{ccc}1& 0& 0\\ 4& 1& 0\\ 10& 4& 1\end{array}\right]; ,\dots ; A^{20}=\left[\begin{array}{ccc}1& 0& 0\\ 20& 1& 0\\ 210& 20& 1\end{array}\right] \left(\because a_{31}=20\mathrm{th} \mathrm{term} \mathrm{in} 1+3+6+10+....\right)$

Hence, sum of the elements of first column$=231$.