## How to solve this problem with Maple...

I need help to solve this problem in maple. :) "Use as many columns of matrix A as possible to construct a matrix B, with the property that the equation Bx=0 has only the trivial solution. Solve Bx=0 to verify you work.." Martix A: A:=matrix([[8,-3,0,-7,2],[-9,4,5,11,-7],[6,-2,2,-4,4],[5,-1.7.0.10]]);

## Plotting during procedure execution...

I was using a procedure for linear systems solution (Gauss-Seidel) and in way to obtain information about the solution convergence I would like to obtain a graph during the procedure execution by Maple that may be ploted in a Maplet window. Does anyone have some suggestion on as I can make this? I am very grateful to anyone who may help.

solve({a1*alpha+b1 *beta=a1^2*alpha+2*a1*a2*gamma+a2^2*gamma*delta/beta,a2*alpha+b2* beta=a1^2*beta+2*a1*a2*delta+a2^2* (beta*gamma-delta*(alpha-delta))/beta, a1*gamma+b1*delta=a1*b1*alpha+a1*b2*gamma+a2*b1*gamma+a2 *b2*gamma*delta/beta,a2*gamma+b2*delta=a1*b1*beta+a1*b2* delta+a2*b1*delta+a2*b2*(beta*gamma-delta*(alpha-delta))/ beta, a1*gamma*delta/beta+b1*(beta*gamma-delta*(alpha-delta))/ beta=b1^2*alpha+2*b1*b2*gamma+b2^2*gamma*delta/beta,a2* gamma*delta/beta+b2*(beta*gamma-delta*(alpha-delta))/ beta=b1^2*beta+2*b1*b2*delta+b2^2*(beta*gamma-delta*( alpha-delta))/beta},{a1,a2,b1,b2}); Warning, computation interrupted

## Old-timer techniques

by: Maple

So you think you really want to know what Maple does? Are you really sure? Well, here is how old-timers do it. [I do not claim that this is either the best or the modern way to do it, just that this is how people with over 10 years of Maple experience do it].

## How to solve this integral?...

I know these two integrals: int(sin(x)/x,x=0..infinity)=Pi/2 and int((sin(x)/x)^2,x=0..infinity)=Pi/2, so I want to know the answer to this integral int((sin(x)/x)^n,x=0..infinity), here n is a positive integer. Only assume(n>0) and additionally(n, integer) and then enter the above statement, Maple could not give an answer. Then I want to know whether there is an exact symbolic result of the integral and if so, how can I get it in Maple. 3x...

## Cross Product Symbol...

I have a question regarding a symbol for cross product. I just uploaded the file referenced at the bottom of this post, and when I viewed it in the file manager it looks different enought from the original file that anyone kind enought to help me will have to download the file. thanks View 2292_CrossProductSymbol.mw on MapleNet or Download 2292_CrossProductSymbol.mw

## Optimize coefficients in a polynomial...

Does anyone have a good idea on how to do this? I have two polynomials alpha := x -> sum('a[k]*x^k','k'=0..N); and beta := x -> sum('b[k]*x^k','k'=0..N);. where N is some constant. I then create a third polynomial g := x -> beta(alpha(x))^2; Then I integrate g(x) from some point to an other point, say -1 to 2: d_tot := int(g(x), x=-1..2); The result is now a 'polynomial' of the indexes a[i] and b[i] from alpha and beta. So far so good but here I'm stuck. Next I would like to choose the indexes a[i] and b[i] for all i=0..N in order to minimize d_tot. Therefore I want Maple to see the a[i]'s and b[i]'s as variables and not coefficients so I can do some manipulations (for instance try minimize(d_tot)).

## To contain Momentum in the Kinetic Energy express...

I am currently working on kinetics area. We have for Kinetic Energy KE = 1/2*m*v^2 and for momentum P= m*v. I need to check for the presence of 'm*v' term in the kinetic Energy expression and want to express Kinetic energy in terms of momentum. That is KE= 1/2*m*v^2 should be expressed as 1/2*P*v after checking for the presence of m*v. The momentum expression should be contained in the formula foe Kinetic energy. Anyone please help me on this Siva

## fsolve...

I am trying to numerically solve the equation (1+j/365)^365=1.1 using command: fsolve((1+j/365)^365=1.1,j); or fsolve((1+j/365)^365=1.1,j,0...1); both cause Maple a lot of problems...cycling. I lost patience. Anyone know how to get the answer?

## output from dsolve...

I have used the dsolve feature and solved a normal ODE. The problem ariss from evaluating that result for different y(x) values. I get the y(x) attached to some message regarding a table. The ODE was y'=-400t*y(t). After solving the diff eq, I evaluated y(t) at t=0 and I got a nice answer, which I defined as t. A few lines later I attempted to use t in a simple subtraction step but got 19.7table[....]... where 19.7 was the correct answer but the subsequent phrase table referred to earlier y(t) evaluation. So, even though t gives a nice answer it can't be used for any calculations. How do I rectify this problem?

## String vibration HELP!...

Hi, Again I'm hearing voices! I have beat myself to death and have found the end of the internet in my search for help on the solutions to String deflection problems: I need to find u(x,t) for the following: Initial velocity = 0, a small k = 0.01, L=1 c^2 = 1 Problem 1 k*(sin(2*Pi*x) ; #Problem 2 k*(sin(Pi*x)-1/3*sin(Pi*3*x)); The second problem is a homework problem. The first is a problem I want to do to see how this works, but I can't grasp the idea. The problems are from the 9th Ed of Kreyszig AEM. (Great for proofs, short on examples)

## Help Understanding Maple Program...

I'm working through an example program. It seems to be working correctly. However, I would like to know why this procedure produces a Maplet ? Any other insight into this procedure you can provide would also be helpful. thanks, View 285_dicegame.mw on MapleNet or Download 285_dicegame.mw
View file details