~~ploting ~~Plotting life history vectors in sage

I'm teaching a math bio class where I need to plot a life history graph. The matrix equation is ~~new=A*old, ~~`new=A*old`

, where ~~A ~~`A`

is a square matrix. I want to create a matrix of the population at each iteration (for say 10 iterations) and plot each column separately. I'm having trouble figuring it out and would appreciate some help.