Chapter 3.4, Problem 61E

In Problems 53-63, set up each system of equations and then solve it using inverse matrices.

$61.$

Attendance Suppose that during the first $2$ weeks of a controversial art exhibit, the daily number of visitors to the gallery is the sum of the numbers of visitors on the previous $3$

days. We represent the numbers of visitors on $3$ successive days by

$N=\left[\begin{array}{c}{n}_t\\ n_{t+1}\\ n_{t+2}\end{array}\right]$

Find the matrix $M$ such that

$MN=\left[\begin{array}{c}{n}_{t+1}\\ n_{t+2}\\ n_t+n_{t+1}+n_{t+2}\end{array}\right]$

If the numbers of visitors on $3$ successive days are given by

$\left[\begin{array}{c}191\\ 346\\ 645\end{array}\right]$

use $M^{-1}$ to find the number of visitors $1$ day earlier (before the $191-$ visitors day).