If A=1 0 01 1 01 1 1 and B=A20 then the sum of the elements of the first column of B is ___

A2=100210321⇒An=100n10∑nn1Given B=A20 Sum of the elements of first column elements of B=1+20+2020+12=231

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If $A = [\begin{array}{l} 1 0 0 \\ 1 1 0 \\ 1 1 1 \end{array}]$ and $B = A^{20}$ then the sum of the elements of the first column of $B$ is ___

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answer is 231.

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Detailed Solution

$A^{2} = [\begin{matrix} 1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 2 & 1 \end{matrix}] \Rightarrow A^{n} = [\begin{matrix} 1 & 0 & 0 \\ n & 1 & 0 \\ \sum n & n & 1 \end{matrix}]$

Given $B = A^{20}$

Sum of the elements of first column elements of $B = 1 + 20 + \frac{20 (20 + 1)}{2} = 231$

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