Let A=pmatrix1&-1&00&1&-10&0&1pmatrix and B=7A^20-20A^7+2I, where I is the identity matrix…

Question

Let $A=\begin{pmatrix}1&-1&0\0&1&-1\0&0&1\end{pmatrix}$ and $B=7A^{20}-20A^7+2I$, where $I$ is the identity matrix of order $3	imes3$. If $B=[b_{ij}]$, then $b_{13}$ is equal to ...

Answer: 910

Accepted Answer

By induction, $A^n=\begin{pmatrix}1&-n&\binom n2\0&1&-n\0&0&1\end{pmatrix}$.

$b_{13}=7\binom{20}2-20\binom72+2(0)=7(190)-20(21)=1330-420=910.$

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