## How can I get the general form for A^k? where A =(...

I try to find a close form for A^k,
where k is an arbitrary interger and A is 2 by 2 matrix as the following:
A = ([[r1*X, (1-r1)*X],[1-r2,r2]]);
r1 and r2 are symbolic constants, X is a variable.

First, I run the following commands in maple:

A:=matrix([[r1*X, (1-r1)*X],[1-r2,r2]]);
Z3:=A^3;
simplify(evalm(Z3),symbolic);

I hope to simplyfy the entries of Z3 in the order of X, i.e.,

z11 = a0*X^3 + a1*X^2 + a2*X +a3;
z12 = ....... (the same as the above)
z21 = .......
z22 = .......

But I do not know how to do it.

I try to find a law for representations of the entries of A^k by looking at the cases k=3,4,....

## Problem with calculating standard deviation symbol...

I am calculating the standard deviation of an function with StandardDeviation command both symbolically and numerically and I get different result for the symbolic and numeric calculation. The result of the symbolic calculation is wrong. Here is my problem: restart;with(Statistics): X := RandomVariable(Uniform(-Pi, Pi)); f:=1/abs(1-0.5*exp(-I*X)); StandardDeviation(f); # It gives 0, which is wrong. StandardDeviation(f, numeric); Re(%); Any idea?

## Need help plotting in spherical coords...

I have a mechanics question with position given by phi = omega t theta = (1/2)Pi * (1+ (1/4)cos(4*omega*t)) r = b This is to be solved in spherical coords. That's not the problem. I solved this just fine, but I would really like to plot this to see what it looks like! Checking the help pages in maple, it says plot3d expects a function r(theta,phi) (might be the other way around?). So, is there a way to plot my 3 parts, or, failing that, how do I turn that into r wrt phi and theta? Cheers Chris PS. How do you post 2D math? I tried, but nothing really worked?

## printing output of all statments inside loop...

How can one print the output from the statements executed within a loop as the loop outputs only the last calculation.

## How do you plot direction fields?...

I was wondering if anyone could tell me how to plot the direction field of a differential equation. I'm trying to plot ty'+2y=sint. If anyone could give me some advice, that'd be great.

## Allowable Trigonometric Function Arguments...

I'm using the cosine function and just read in the help section that the trig functions only take arguments in radians. Is this true ? Is there no way to use arguments in degrees for the trig functions ? v/r, Dan

## Removing extra spaces in a string...

Hi, If a sentence (as a string) is given with uneven number of spaces in it, how can we smooth it out so that every word is followed by exactly one space. I think this would be solved by Regular Expression in patmatch, but exactly I don't know. Kindly help me. Thanks.

## multi plot...

i have two function f(x) and g(x) and i wanna plot them in one plot x=1200..2300, but for f(x) y=0..600 and for g(x) y=0..50. How can i display different scaling y-axis?

## 2D and 3D in the same graph...

Hi, I would like some help with plotting a 2D and 3D graph together. I actually have an equation with two varying parameters and I have displayed a 3D plot.What i want is to set a value for the one parameter and plot the line together with the previous surface, so that I can see where this line is placed on the surface.I provide the example to make myself clearer. Itouch50 := -0.4058074876e13*sqrt(1.+h)/(sqrt(ts)*(-500000000.0*ln((625.+125.*h+25.*h^2+5.*h^3)/h)* sqrt(1.+h)+587311661.7)) Itouch := 474335.0379*h*(10300.*2.718281828^(-3.703703704*ts)+1030.*2.718281828^(-3.703703704*ts)* h+490.*2.718281828^(1/(5.*ts+6.))+49.*2.718281828^(1/(5.*ts+6.))*h)/(51200.*sqrt(ln(100.*h))*h+5120.*sqrt(ln(100.*h))*h^2+25600.+12790.*h+511.*h^2)

## Need help simplifying this equation...

Hello, I have never used Maple before and I am working on an assignment but unfortunately class ended before I could ask my professor with some help so I was hoping someone on here might be able to help me out. All I need to do is get the first equation to look like the second equation, I would use the simplify command but I cannot break apart the l(l+1), can anyone help me out?

Equation 1: Need it to look like this: View file details

## How do you make a general function ie f(x,y,z)...

I want to tell maple that func is a function of x, y, z, but I don't know what the function is. This is so when maple evaluates derivatives, etc, it won't assume 'func' is a constant. ie: instead of func := (x,y,z) -> x^2 + 2y + 3xyz; I just want to say func : = (x,y,z); so that when I ask for a derivative, maple just prints out 'diff(func, x, 1) etc, where 'diff(func, x, 1) means the first partial deriv of x. I hope that's clear enough for all you experts out there. I am a newbie to Maple. I tried func : = (x,y,z); but it did not seem to work for me.... Thanks in advance,

## Unassign from within a procedure...

Hello. I was wondering if it is possible to unassign a variable from within a procedure. The accompanying file illustrates what I am trying to do. As always, my anticipated thanks to anyone kind enough to take the time to help me. I would be totally lost in MAPLE without this forum. a href='http://maplenet.maplesoft.com/maplenet/worksheet/mapleprimes/2292_Unassign within a procedure.mw'>View 2292_Unassign within a procedure.mw on MapleNet or Download 2292_Unassign within a procedure.mw

## converting matlab or c code to maple?...

Hi, I'm new to maple and I would like to draw a plot of a time-dependent 2D Vectorfield and some trajectories: 1. I have the field udep := (x, y, t) -> cos(t)*x - sin(t)* (-y); vdep := (x, y, t) -> sin(t)*x + cos(t)* (-y); it looks like this: 2. now i would like to draw a trajectory T that has at every point a tangent parallel to the field (to show the path of a massless particle inside this field)