Assuming I have the sequence $(a_n)_{n=1}^\infty$ defined by $a_n=a_{n-1}+6a_{n-2}$, I need to find a matrix $2$x$2$ corresponding to the given sequence.
I know the answer, but I don't understand why this is it.
Will appreciate some explanation.
Thanks a lot!
Judging from the document shared by @TeresaLisbon, you want to find a matrix $M$ such that$$\begin{bmatrix}a_n\\a_{n-1}\end{bmatrix}=M\begin{bmatrix}a_{n-1}\\a_{n-2}\end{bmatrix}$$We know that $a_n=a_{n-1}+6a_{n-2}$, so the first row of $M$ is $[1,6]$. And $a_{n-1}=1a_{n-1}+0a_{n-2}$, so the second row is $[1,0]$, giving:$$M=\begin{bmatrix}1&6\\1&0\end{bmatrix}$$