$9)$

$E_{t+1}=120A_t$

$L_{t+1}=\frac{1}{5}{E}_t$

$A_{t+1}=\frac{1}{26}{L}_t$

a$.$ Express this model as $x_{t+1}=P*x_t,$ using a $33$ matrix $P.$ What is $x$

b$.$ What type of projection matrix is $P?$

c$.$ Compute $P^2$ and $P^3,$ what is the biological meaning of these matrices

d$.$ Will the insect population increase or decrease?