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These are questions asked by cuongtd

Hello everybody,

I would like to ask: How many ways to impose the rank deficiency of a matrix J?

1. First is the determinant(J) = 0

2. Multiply with a non-zero vector V: so that we have J*V = 0;

3. be listed......


something about the minors of the matrix? 

I hope to have as many methods as possible!

Hello everybody,

I have an interesting math problem, here it is:


Add the following operators: +, -, * in the middle of the following string 123456789 to get the final result: 2016

The operators can be added randomly at any place, it isn't necessarily placed in between single numbers.


To convince your result, one should provide the code or explain explicitly your method.

Have fun!!!!



Hello, I have the system of equations in many vars as below, I want to make an implicit plot in Maple with the projection on 3 vars, for example, in this case (x,y,t1). The range is x[-10,10], y[-10,10], t1[-Pi,Pi] and the rest of the vars are [-Pi,Pi]. Does anyone know how to do it? We have also the inequalities in the system.


f1:= cos(t1)+1.35*cos(p1)-x;

f2:= sin(t1)+1.35*sin(p1)-y;

f3:= cos(t2)+1.35*cos(p2)-x +1.15;

f4:= sin(t2)+1.35*sin(p2)-y;

f5:= cos(t3)+1.35*cos(p3)-x+0.575;

f6:= sin(t3)+1.35*sin(p3)-y +0.995;

f7:= cos(t1)*cos(t2)*cos(t3)*sin(p1)*sin(p2)*sin(p3)-cos(t1)*cos(t2)*sin(t3)*sin(p1)*sin(p2)*cos(p3)-cos(t1)*sin(t2)*cos(t3)*sin(p1)*cos(p2)*sin(p3)+cos(t1)*sin(t2)*sin(t3)*sin(p1)*cos(p2)*cos(p3)-sin(t1)*cos(t2)*cos(t3)*cos(p1)*sin(p2)*sin(p3)+sin(t1)*cos(t2)*sin(t3)*cos(p1)*sin(p2)*cos(p3)+sin(t1)*sin(t2)*cos(t3)*cos(p1)*cos(p2)*sin(p3)-sin(t1)*sin(t2)*sin(t3)*cos(p1)*cos(p2)*cos(p3);

f8:= cos(t1)*sin(p1)-sin(t1)*cos(p1) >= 0;

f9:= cos(t2)*sin(p2)-sin(t2)*cos(p2) >= 0;

f10:= cos(t3)*sin(p3)-sin(t3)*cos(p3) >= 0;


This is the system of equations in term of sin and cos. I have used the command "solve" in Maple but it yielded only 2 solutions. I've tried to use with(RealDomain): It yielded more solutions but most of them were wrong.



f1 := -8100+(-30+70*cos(t1)-40*cos(t2))^2+(-70*sin(t1)+40*sin(t2))^2

f2 := (-20-80*cos(t3))^2+(-15+70*cos(t1)+10*cos(t1+t))^2+(-70*sin(t1)-10*sin(t1+t)+80*sin(t3))^2-5625

f3 := (-20-80*cos(t3))^2+(15+40*cos(t2)+10*cos(t1+t))^2+(-40*sin(t2)-10*sin(t1+t)+80*sin(t3))^2-5625

f4 := 10*cos(t1+t)*(30-70*cos(t1)+40*cos(t2))-10*sin(t1+t)*(70*sin(t1)-40*sin(t2))


Anybody know how to solve this system of equations to get the full set of roots?

Thank you very much in advance.

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