I am having problem in solving symbolic 11x11 matrix
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Hi,
I need to find eigen values of a 11x11 matrix. I tried to solve it on matlab but unfortunately whenever i try to find the eigenvalues using function eig or determinant using determinant function, MATLAB just keep on saying that it is busy. The solution is on for almost 10 days and so far I have received no result. I am attaching the program with this querry. If anyone can help it would be really helpful thank you.
clear all;
syms a b c C11c C12c C13c C21c C22c C23c C31c C32c C33c C44c C55c C66c ft fb ...
C11t C12t C13t C21t C22t C23t C31t C32t C33t C55t C66t C11b C12b ...
C13b C21b C22b C23b C31b C32b C33b C55b C66b ktP Klc A B
Klc=[[(47/30).*c.^(-1).*C55c+(6/35).*a.^(-2).*b.^(-2).*c.*(b.^2.*C11c+ ...
a.^2.*C66c).*pi.^2+(a.^(-2).*C11t+b.^(-2).*C66t).*ft.*pi.^2;( ...
-7/30).*c.^(-1).*C55c+(1/35).*a.^(-2).*b.^(-2).*c.*(b.^2.*C11c+ ...
a.^2.*C66c).*pi.^2;(-4/3).*c.^(-1).*C55c+(2/15).*a.^(-2).*b.^(-2) ...
.*c.*(b.^2.*C11c+a.^2.*C66c).*pi.^2;(2/35).*((-14).*C55c+c.^2.*( ...
a.^(-2).*C11c+b.^(-2).*C66c).*pi.^2);(1/35).*a.^(-1).*b.^(-1).*( ...
6.*c.*(C12c+C66c)+35.*(C12t+C66t).*ft).*pi.^2;(1/35).*a.^(-1).* ...
b.^(-1).*c.*(C12c+C66c).*pi.^2;(2/15).*a.^(-1).*b.^(-1).*c.*(C12c+ ...
C66c).*pi.^2;(-2/35).*a.^(-1).*b.^(-1).*c.^2.*(C12c+C66c).*pi.^2;( ...
1/60).*a.^(-1).*c.^(-1).*((-22).*c.*C13c+38.*c.*C55c+47.*C55c.*ft) ...
.*pi+(3/35).*a.^(-3).*b.^(-2).*c.*(b.^2.*C11c+a.^2.*(C12c+2.*C66c) ...
).*ft.*pi.^3;(1/420).*a.^(-3).*c.^(-1).*pi.*((-6).*c.^2.*C11c.* ...
fb.*pi.^2+a.^2.*((-14).*c.*(C13c+C55c)+49.*C55c.*fb+(-6).*b.^(-2) ...
.*c.^2.*(C12c+2.*C66c).*fb.*pi.^2));(2/5).*a.^(-1).*(C13c+C55c).* ...
pi],[(-7/30).*c.^(-1).*C55c+(1/35).*a.^(-2).*b.^(-2).*c.*(b.^2.* ...
C11c+a.^2.*C66c).*pi.^2;(47/30).*c.^(-1).*C55c+(6/35).*a.^(-2).* ...
b.^(-2).*c.*(b.^2.*C11c+a.^2.*C66c).*pi.^2+(a.^(-2).*C11b+b.^(-2) ...
.*C66b).*fb.*pi.^2;(-4/3).*c.^(-1).*C55c+(2/15).*a.^(-2).*b.^(-2) ...
.*c.*(b.^2.*C11c+a.^2.*C66c).*pi.^2;(4/5).*C55c+(-2/35).*a.^(-2).* ...
b.^(-2).*c.^2.*(b.^2.*C11c+a.^2.*C66c).*pi.^2;(1/35).*a.^(-1).* ...
b.^(-1).*c.*(C12c+C66c).*pi.^2;(1/35).*a.^(-1).*b.^(-1).*(6.*c.*( ...
C12c+C66c)+35.*(C12b+C66b).*fb).*pi.^2;(2/15).*a.^(-1).*b.^(-1).* ...
c.*(C12c+C66c).*pi.^2;(2/35).*a.^(-1).*b.^(-1).*c.^2.*(C12c+C66c) ...
.*pi.^2;(1/420).*a.^(-3).*c.^(-1).*(6.*c.^2.*C11c.*ft.*pi.^3+ ...
a.^2.*pi.*(14.*c.*(C13c+C55c)+(-49).*C55c.*ft+6.*b.^(-2).*c.^2.*( ...
C12c+2.*C66c).*ft.*pi.^2));(1/60).*a.^(-1).*c.^(-1).*(22.*c.*C13c+ ...
(-38).*c.*C55c+(-47).*C55c.*fb).*pi+(-3/35).*a.^(-3).*b.^(-2).*c.* ...
(b.^2.*C11c+a.^2.*(C12c+2.*C66c)).*fb.*pi.^3;(-2/5).*a.^(-1).*( ...
C13c+C55c).*pi],[(-4/3).*c.^(-1).*C55c+(2/15).*a.^(-2).*b.^(-2).* ...
c.*(b.^2.*C11c+a.^2.*C66c).*pi.^2;(-4/3).*c.^(-1).*C55c+(2/15).* ...
a.^(-2).*b.^(-2).*c.*(b.^2.*C11c+a.^2.*C66c).*pi.^2;(8/3).*c.^(-1) ...
.*C55c+(16/15).*c.*(a.^(-2).*C11c+b.^(-2).*C66c).*pi.^2;0;(2/15).* ...
a.^(-1).*b.^(-1).*c.*(C12c+C66c).*pi.^2;(2/15).*a.^(-1).*b.^(-1).* ...
c.*(C12c+C66c).*pi.^2;(16/15).*a.^(-1).*b.^(-1).*c.*(C12c+C66c).* ...
pi.^2;0;(1/15).*a.^(-3).*c.^(-1).*(c.^2.*C11c.*ft.*pi.^3+a.^2.* ...
pi.*((-10).*(c.*(C13c+C55c)+C55c.*ft)+b.^(-2).*c.^2.*(C12c+2.* ...
C66c).*ft.*pi.^2));(2/3).*a.^(-1).*c.^(-1).*(c.*(C13c+C55c)+C55c.* ...
fb).*pi+(-1/15).*a.^(-3).*b.^(-2).*c.*(b.^2.*C11c+a.^2.*(C12c+2.* ...
C66c)).*fb.*pi.^3;0],[(2/35).*((-14).*C55c+c.^2.*(a.^(-2).*C11c+ ...
b.^(-2).*C66c).*pi.^2);(4/5).*C55c+(-2/35).*a.^(-2).*b.^(-2).* ...
c.^2.*(b.^2.*C11c+a.^2.*C66c).*pi.^2;0;(8/105).*c.*(21.*C55c+2.* ...
c.^2.*(a.^(-2).*C11c+b.^(-2).*C66c).*pi.^2);(2/35).*a.^(-1).*b.^( ...
-1).*c.^2.*(C12c+C66c).*pi.^2;(-2/35).*a.^(-1).*b.^(-1).*c.^2.*( ...
C12c+C66c).*pi.^2;0;(-16/105).*a.^(-1).*b.^(-1).*c.^3.*(C12c+C66c) ...
.*pi.^2;(-2/15).*a.^(-1).*(2.*c.*(C13c+C55c)+3.*C55c.*ft).*pi+( ...
1/35).*a.^(-3).*b.^(-2).*c.^2.*(b.^2.*C11c+a.^2.*(C12c+2.*C66c)).* ...
ft.*pi.^3;(-2/15).*a.^(-1).*(2.*c.*(C13c+C55c)+3.*C55c.*fb).*pi+( ...
1/35).*a.^(-3).*b.^(-2).*c.^2.*(b.^2.*C11c+a.^2.*(C12c+2.*C66c)).* ...
fb.*pi.^3;(8/15).*a.^(-1).*c.*(C13c+C55c).*pi],[(1/35).*a.^(-1).* ...
b.^(-1).*(6.*c.*(C12c+C66c)+35.*(C12t+C66t).*ft).*pi.^2;(1/35).* ...
a.^(-1).*b.^(-1).*c.*(C12c+C66c).*pi.^2;(2/15).*a.^(-1).*b.^(-1).* ...
c.*(C12c+C66c).*pi.^2;(2/35).*a.^(-1).*b.^(-1).*c.^2.*(C12c+C66c) ...
.*pi.^2;(47/30).*c.^(-1).*C44c+(6/35).*a.^(-2).*b.^(-2).*c.*( ...
a.^2.*C22c+b.^2.*C66c).*pi.^2+(b.^(-2).*C22t+a.^(-2).*C66t).*ft.* ...
pi.^2;(-7/30).*c.^(-1).*C44c+(1/35).*a.^(-2).*b.^(-2).*c.*(a.^2.* ...
C22c+b.^2.*C66c).*pi.^2;(-4/3).*c.^(-1).*C44c+(2/15).*a.^(-2).* ...
b.^(-2).*c.*(a.^2.*C22c+b.^2.*C66c).*pi.^2;(4/5).*C44c+(-2/35).* ...
a.^(-2).*b.^(-2).*c.^2.*(a.^2.*C22c+b.^2.*C66c).*pi.^2;(1/60).* ...
b.^(-1).*c.^(-1).*((-22).*c.*C23c+38.*c.*C44c+47.*C44c.*ft).*pi+( ...
3/35).*a.^(-2).*b.^(-3).*c.*(a.^2.*C22c+b.^2.*(C12c+2.*C66c)).* ...
ft.*pi.^3;(1/420).*b.^(-3).*c.^(-1).*pi.*((-6).*c.^2.*C22c.*fb.* ...
pi.^2+b.^2.*((-14).*c.*(C23c+C44c)+49.*C44c.*fb+(-6).*a.^(-2).* ...
c.^2.*(C12c+2.*C66c).*fb.*pi.^2));(2/5).*b.^(-1).*(C23c+C44c).* ...
pi],[(1/35).*a.^(-1).*b.^(-1).*c.*(C12c+C66c).*pi.^2;(1/35).*a.^( ...
-1).*b.^(-1).*(6.*c.*(C12c+C66c)+35.*(C12b+C66b).*fb).*pi.^2;( ...
2/15).*a.^(-1).*b.^(-1).*c.*(C12c+C66c).*pi.^2;(-2/35).*a.^(-1).* ...
b.^(-1).*c.^2.*(C12c+C66c).*pi.^2;(-7/30).*c.^(-1).*C44c+(1/35).* ...
a.^(-2).*b.^(-2).*c.*(a.^2.*C22c+b.^2.*C66c).*pi.^2;(47/30).*c.^( ...
-1).*C44c+(6/35).*a.^(-2).*b.^(-2).*c.*(a.^2.*C22c+b.^2.*C66c).* ...
pi.^2+(b.^(-2).*C22b+a.^(-2).*C66b).*fb.*pi.^2;(-4/3).*c.^(-1).* ...
C44c+(2/15).*a.^(-2).*b.^(-2).*c.*(a.^2.*C22c+b.^2.*C66c).*pi.^2;( ...
2/35).*((-14).*C44c+c.^2.*(b.^(-2).*C22c+a.^(-2).*C66c).*pi.^2);( ...
1/420).*b.^(-3).*c.^(-1).*(6.*c.^2.*C22c.*ft.*pi.^3+b.^2.*pi.*( ...
14.*c.*(C23c+C44c)+(-49).*C44c.*ft+6.*a.^(-2).*c.^2.*(C12c+2.* ...
C66c).*ft.*pi.^2));(1/60).*b.^(-1).*c.^(-1).*(22.*c.*C23c+(-38).* ...
c.*C44c+(-47).*C44c.*fb).*pi+(-3/35).*a.^(-2).*b.^(-3).*c.*(a.^2.* ...
C22c+b.^2.*(C12c+2.*C66c)).*fb.*pi.^3;(-2/5).*b.^(-1).*(C23c+C44c) ...
.*pi],[(2/15).*a.^(-1).*b.^(-1).*c.*(C12c+C66c).*pi.^2;(2/15).* ...
a.^(-1).*b.^(-1).*c.*(C12c+C66c).*pi.^2;(16/15).*a.^(-1).*b.^(-1) ...
.*c.*(C12c+C66c).*pi.^2;0;(-4/3).*c.^(-1).*C44c+(2/15).*a.^(-2).* ...
b.^(-2).*c.*(a.^2.*C22c+b.^2.*C66c).*pi.^2;(-4/3).*c.^(-1).*C44c+( ...
2/15).*a.^(-2).*b.^(-2).*c.*(a.^2.*C22c+b.^2.*C66c).*pi.^2;(8/3).* ...
c.^(-1).*C44c+(16/15).*c.*(b.^(-2).*C22c+a.^(-2).*C66c).*pi.^2;0;( ...
1/15).*b.^(-3).*c.^(-1).*(c.^2.*C22c.*ft.*pi.^3+b.^2.*pi.*((-10).* ...
(c.*(C23c+C44c)+C44c.*ft)+a.^(-2).*c.^2.*(C12c+2.*C66c).*ft.* ...
pi.^2));(2/3).*b.^(-1).*c.^(-1).*(c.*(C23c+C44c)+C44c.*fb).*pi+( ...
-1/15).*a.^(-2).*b.^(-3).*c.*(a.^2.*C22c+b.^2.*(C12c+2.*C66c)).* ...
fb.*pi.^3;0],[(-2/35).*a.^(-1).*b.^(-1).*c.^2.*(C12c+C66c).*pi.^2; ...
(2/35).*a.^(-1).*b.^(-1).*c.^2.*(C12c+C66c).*pi.^2;0;(-16/105).* ...
a.^(-1).*b.^(-1).*c.^3.*(C12c+C66c).*pi.^2;(4/5).*C44c+(-2/35).* ...
a.^(-2).*b.^(-2).*c.^2.*(a.^2.*C22c+b.^2.*C66c).*pi.^2;(2/35).*(( ...
-14).*C44c+c.^2.*(b.^(-2).*C22c+a.^(-2).*C66c).*pi.^2);0;(8/105).* ...
c.*(21.*C44c+2.*c.^2.*(b.^(-2).*C22c+a.^(-2).*C66c).*pi.^2);(2/15) ...
.*b.^(-1).*(2.*c.*(C23c+C44c)+3.*C44c.*ft).*pi+(-1/35).*a.^(-2).* ...
b.^(-3).*c.^2.*(a.^2.*C22c+b.^2.*(C12c+2.*C66c)).*ft.*pi.^3;(2/15) ...
.*b.^(-1).*(2.*c.*(C23c+C44c)+3.*C44c.*fb).*pi+(-1/35).*a.^(-2).* ...
b.^(-3).*c.^2.*(a.^2.*C22c+b.^2.*(C12c+2.*C66c)).*fb.*pi.^3;( ...
-8/15).*b.^(-1).*c.*(C23c+C44c).*pi],[(1/60).*a.^(-1).*c.^(-1).*(( ...
-22).*c.*C13c+38.*c.*C55c+47.*C55c.*ft).*pi+(3/35).*a.^(-3).*b.^( ...
-2).*c.*(b.^2.*C11c+a.^2.*(C12c+2.*C66c)).*ft.*pi.^3;(1/420).*a.^( ...
-3).*c.^(-1).*(6.*c.^2.*C11c.*ft.*pi.^3+a.^2.*pi.*(14.*c.*(C13c+ ...
C55c)+(-49).*C55c.*ft+6.*b.^(-2).*c.^2.*(C12c+2.*C66c).*ft.*pi.^2) ...
);(1/15).*a.^(-3).*c.^(-1).*(c.^2.*C11c.*ft.*pi.^3+a.^2.*pi.*(( ...
-10).*(c.*(C13c+C55c)+C55c.*ft)+b.^(-2).*c.^2.*(C12c+2.*C66c).* ...
ft.*pi.^2));(-2/15).*a.^(-1).*(2.*c.*(C13c+C55c)+3.*C55c.*ft).*pi+ ...
(1/35).*a.^(-3).*b.^(-2).*c.^2.*(b.^2.*C11c+a.^2.*(C12c+2.*C66c)) ...
.*ft.*pi.^3;(1/60).*b.^(-1).*c.^(-1).*((-22).*c.*C23c+38.*c.*C44c+ ...
47.*C44c.*ft).*pi+(3/35).*a.^(-2).*b.^(-3).*c.*(a.^2.*C22c+b.^2.*( ...
C12c+2.*C66c)).*ft.*pi.^3;(1/420).*b.^(-3).*c.^(-1).*(6.*c.^2.* ...
C22c.*ft.*pi.^3+b.^2.*pi.*(14.*c.*(C23c+C44c)+(-49).*C44c.*ft+6.* ...
a.^(-2).*c.^2.*(C12c+2.*C66c).*ft.*pi.^2));(1/15).*b.^(-3).*c.^( ...
-1).*(c.^2.*C22c.*ft.*pi.^3+b.^2.*pi.*((-10).*(c.*(C23c+C44c)+ ...
C44c.*ft)+a.^(-2).*c.^2.*(C12c+2.*C66c).*ft.*pi.^2));(2/15).*b.^( ...
-1).*(2.*c.*(C23c+C44c)+3.*C44c.*ft).*pi+(-1/35).*a.^(-2).*b.^(-3) ...
.*c.^2.*(a.^2.*C22c+b.^2.*(C12c+2.*C66c)).*ft.*pi.^3;(1/840).*a.^( ...
-4).*b.^(-4).*c.^(-1).*(980.*a.^4.*b.^4.*C33c+7.*a.^2.*b.^2.*( ...
a.^2.*(32.*c.^2.*C44c+47.*C44c.*ft.^2+(-4).*c.*(11.*C23c.*ft+(-19) ...
.*C44c.*ft+30.*ktP))+b.^2.*(32.*c.^2.*C55c+47.*C55c.*ft.^2+(-4).* ...
c.*(11.*C13c.*ft+(-19).*C55c.*ft+30.*ktP))).*pi.^2+2.*c.*ft.^2.*( ...
18.*c.*(b.^4.*C11c+a.^4.*C22c+2.*a.^2.*b.^2.*(C12c+2.*C66c))+35.*( ...
b.^4.*C11t+a.^4.*C22t+2.*a.^2.*b.^2.*(C12t+2.*C66t)).*ft).*pi.^4); ...
(1/840).*a.^(-4).*b.^(-4).*c.^(-1).*(140.*a.^4.*b.^4.*C33c+(-7).* ...
a.^2.*b.^2.*(a.^2.*(8.*c.^2.*C44c+(-7).*C44c.*fb.*ft+2.*c.*(C23c+ ...
C44c).*(fb+ft))+b.^2.*(8.*c.^2.*C55c+(-7).*C55c.*fb.*ft+2.*c.*( ...
C13c+C55c).*(fb+ft))).*pi.^2+(-6).*c.^2.*(b.^4.*C11c+a.^4.*C22c+ ...
2.*a.^2.*b.^2.*(C12c+2.*C66c)).*fb.*ft.*pi.^4);(1/15).*((-20).* ...
c.^(-1).*C33c+2.*c.*(b.^(-2).*C44c+a.^(-2).*C55c).*pi.^2+3.*(b.^( ...
-2).*(C23c+C44c)+a.^(-2).*(C13c+C55c)).*ft.*pi.^2)],[(1/420).*a.^( ...
-3).*c.^(-1).*pi.*((-6).*c.^2.*C11c.*fb.*pi.^2+a.^2.*((-14).*c.*( ...
C13c+C55c)+49.*C55c.*fb+(-6).*b.^(-2).*c.^2.*(C12c+2.*C66c).*fb.* ...
pi.^2));(1/60).*a.^(-1).*c.^(-1).*(22.*c.*C13c+(-38).*c.*C55c+( ...
-47).*C55c.*fb).*pi+(-3/35).*a.^(-3).*b.^(-2).*c.*(b.^2.*C11c+ ...
a.^2.*(C12c+2.*C66c)).*fb.*pi.^3;(2/3).*a.^(-1).*c.^(-1).*(c.*( ...
C13c+C55c)+C55c.*fb).*pi+(-1/15).*a.^(-3).*b.^(-2).*c.*(b.^2.* ...
C11c+a.^2.*(C12c+2.*C66c)).*fb.*pi.^3;(-2/15).*a.^(-1).*(2.*c.*( ...
C13c+C55c)+3.*C55c.*fb).*pi+(1/35).*a.^(-3).*b.^(-2).*c.^2.*( ...
b.^2.*C11c+a.^2.*(C12c+2.*C66c)).*fb.*pi.^3;(1/420).*b.^(-3).*c.^( ...
-1).*pi.*((-6).*c.^2.*C22c.*fb.*pi.^2+b.^2.*((-14).*c.*(C23c+C44c) ...
+49.*C44c.*fb+(-6).*a.^(-2).*c.^2.*(C12c+2.*C66c).*fb.*pi.^2));( ...
1/60).*b.^(-1).*c.^(-1).*(22.*c.*C23c+(-38).*c.*C44c+(-47).*C44c.* ...
fb).*pi+(-3/35).*a.^(-2).*b.^(-3).*c.*(a.^2.*C22c+b.^2.*(C12c+2.* ...
C66c)).*fb.*pi.^3;(2/3).*b.^(-1).*c.^(-1).*(c.*(C23c+C44c)+C44c.* ...
fb).*pi+(-1/15).*a.^(-2).*b.^(-3).*c.*(a.^2.*C22c+b.^2.*(C12c+2.* ...
C66c)).*fb.*pi.^3;(2/15).*b.^(-1).*(2.*c.*(C23c+C44c)+3.*C44c.*fb) ...
.*pi+(-1/35).*a.^(-2).*b.^(-3).*c.^2.*(a.^2.*C22c+b.^2.*(C12c+2.* ...
C66c)).*fb.*pi.^3;(1/840).*a.^(-4).*b.^(-4).*c.^(-1).*(140.*a.^4.* ...
b.^4.*C33c+(-7).*a.^2.*b.^2.*(a.^2.*(8.*c.^2.*C44c+(-7).*C44c.* ...
fb.*ft+2.*c.*(C23c+C44c).*(fb+ft))+b.^2.*(8.*c.^2.*C55c+(-7).* ...
C55c.*fb.*ft+2.*c.*(C13c+C55c).*(fb+ft))).*pi.^2+(-6).*c.^2.*( ...
b.^4.*C11c+a.^4.*C22c+2.*a.^2.*b.^2.*(C12c+2.*C66c)).*fb.*ft.* ...
pi.^4);(1/840).*a.^(-4).*b.^(-4).*c.^(-1).*(980.*a.^4.*b.^4.*C33c+ ...
7.*a.^2.*b.^2.*(a.^2.*(32.*c.^2.*C44c+47.*C44c.*fb.^2+(-4).*c.*( ...
11.*C23c.*fb+(-19).*C44c.*fb+30.*ktP))+b.^2.*(32.*c.^2.*C55c+47.* ...
C55c.*fb.^2+(-4).*c.*(11.*C13c.*fb+(-19).*C55c.*fb+30.*ktP))).* ...
pi.^2+2.*c.*fb.^2.*(18.*c.*(b.^4.*C11c+a.^4.*C22c+2.*a.^2.*b.^2.*( ...
C12c+2.*C66c))+35.*(b.^4.*C11b+a.^4.*C22b+2.*a.^2.*b.^2.*(C12b+2.* ...
C66b)).*fb).*pi.^4);(1/15).*((-20).*c.^(-1).*C33c+2.*c.*(b.^(-2).* ...
C44c+a.^(-2).*C55c).*pi.^2+3.*(b.^(-2).*(C23c+C44c)+a.^(-2).*( ...
C13c+C55c)).*fb.*pi.^2)],[(2/5).*a.^(-1).*(C13c+C55c).*pi;(-2/5).* ...
a.^(-1).*(C13c+C55c).*pi;0;(8/15).*a.^(-1).*c.*(C13c+C55c).*pi;( ...
2/5).*b.^(-1).*(C23c+C44c).*pi;(-2/5).*b.^(-1).*(C23c+C44c).*pi;0; ...
(-8/15).*b.^(-1).*c.*(C23c+C44c).*pi;(1/15).*((-20).*c.^(-1).* ...
C33c+2.*c.*(b.^(-2).*C44c+a.^(-2).*C55c).*pi.^2+3.*(b.^(-2).*( ...
C23c+C44c)+a.^(-2).*(C13c+C55c)).*ft.*pi.^2);(1/15).*((-20).*c.^( ...
-1).*C33c+2.*c.*(b.^(-2).*C44c+a.^(-2).*C55c).*pi.^2+3.*(b.^(-2).* ...
(C23c+C44c)+a.^(-2).*(C13c+C55c)).*fb.*pi.^2);(8/3).*c.^(-1).* ...
C33c+(16/15).*c.*(b.^(-2).*C44c+a.^(-2).*C55c).*pi.^2]];
%Check symmetry of matrix
% A= transpose(Klc);
% M=Klc-A;
% Determinant of Klc
Det= solve(det(Klc))
2 Comments
Ameer Hamza
on 28 Nov 2020
Solving such a complicated matrix symbolically is not a good strategy. Especially considering that you have a single equation and several unknowns. Your system is under-determined, and there can be a potentially infinite number of solutions. Using numerical techniques are better for such problems. Can you explain the background of this problem? Maybe we can suggest some alternative solution.
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