Matrix Plot – Little Exercise

Question

Hi there, mathematicians.

I'm not very good at coding plots in Mathematica, so I was hoping that one of you could help me solve a problem I'm having.

I have the following matrix plot:

Z = {Subscript[x, 0], Subscript[x, 1], Subscript[x, 2]}
X = {{0, 8, 12}, {.1, 0, 0}, {0, .2, 0}}

Then I put it in a function as follows:

P[x_] := X^x.Z

I would like Mathematica to display plots such that, whenever x iterates from 1 to 10 in the function, the x1, x2, and x3 from the matrix are respectively plotted in three plots. Can anyone help me?

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EDIT: Trying to be more clear

I have the matrix (mat) and the vector (v):

mat = {{0, 8, 12}, {.1, 0, 0}, {0, .2, 0}}
v = {x0, x1, x2}

Then later I define the function for population development, pD, taking t (for time in days) as its only parameter.

pD[t] = mat^t.v

Now I would like to show the development of the variables $x_1$,$x_2$, and $x_3$ assuming the values 30, 60, 30, respectively. I would do so by making plots of the three functions over the range 1 to 10 days. For each the first plot should display the values of $\{t,pD[t_{x_1}]\}$, the second the values of $\{t,pD[t_{x_2}]\}$, and the third the values of $\{t,pD[t_{x_3}]\}$. I hope this clarifies my question. Sorry for being so unconventional in the first place. However, having worked my eyes blind for quite some time, I presumed that it was anything but difficult to understand. Thanks for your patience!

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Best regards, Brinck10

Answer 1

Assuming you want mat^t to mean the matrix power, one way to plot the three elements of the output is to make a table of the values and then ListPlot them:

 pD[t_] := MatrixPower[mat, t].{30, 60, 30};
 ListLinePlot[Transpose[Table[pD[t], {t, 1, 10, 1}]]]

Answer 2

I am posting this, just to have something to use to try to converge to an answer. Since I am not sure I still understand the question.

This just plots a vector in 3D. i.e a line from $(0,0,0)$ to the another point in 3D space. The other point is the result of doing $mat^n.vec$. where mat matrix and vec is vector. And the question asked to plot this for each $n$

I have a feeling I am missing something here. But at least now we have something to change to try to find out what is actually needed :)

Manipulate[
 Module[{vec, mat, pt},
  vec = {30, 60, 30};
  mat = {{0, 8, 12}, {.1, 0, 0}, {0, .2, 0}};
  pt = p[n, mat, vec];

  Graphics3D[
   {Thick, Line[{{0, 0, 0}, p[n, mat, vec]}]}, Axes -> True
   ]

  ],

 {{n, 2, "n="}, 1, 10, 1},
 Initialization :>
  (
   p[n_, mat_, vec_] := mat^n.vec
   )
 ]