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I am attempting to evaluate a matrix multiplication, then extract 4 specific cells from the resultant matrix and create a new 2x2 matrix with these 4 specific cells. I then need to calculate the points at which the determinant of the 2x2 matrix equals zero. This is to solve the resonant frequency of transverse vibration of a beam. My attempt at doing this:

e,f,g,h,i,j,k,l,m,n,o,p,g,r,s,t=var('e,f,g,h,i,j,k,l,m,n,o,p,g,r,s,t') var("w", domain="complex") a=4 b=8 c=32/3 d=4

m1=1 m2=m1/2 x=m1(w) y=m2(w)

F=matrix([[1,a,b,c],[0,1,d,b],[0,0,1,a],[0,0,0,1]]) M1=matrix([[1,0,0,0],[0,1,0,0],[0,0,1,0],[x,0,0,1]]) M2=matrix([[1,0,0,0],[0,1,0,0],[0,0,1,0],[y,0,0,1]]) ([[e,f,g,h],[i,j,k,l],[m,n,o,p],[q,r,s,t]])=FM1FM1FM1F*M2 A=matrix([[o,p],[s,t]]) B=A.determinant() C=solve(B==0,w) numerical_approx(C)

Sagemath returns an error since there are complex numbers.

I require numerical solutions.

apologies if the question is unclear, I have zero programming background, this is for my engineering dissertation.

Any help is appreciated.

I am attempting to evaluate a matrix multiplication, then extract 4 specific cells from the resultant matrix and create a new 2x2 matrix with these 4 specific cells. I then need to calculate the points at which the determinant of the 2x2 matrix equals zero. This is to solve the resonant frequency of transverse vibration of a beam. My attempt at doing this:

e,f,g,h,i,j,k,l,m,n,o,p,g,r,s,t=var('e,f,g,h,i,j,k,l,m,n,o,p,g,r,s,t') e,f,g,h,i,j,k,l,m,n,o,p,g,r,s,t=var('e,f,g,h,i,j,k,l,m,n,o,p,g,r,s,t'); var("w", domain="complex") a=4 b=8 c=32/3 d=4domain="complex"); a=4; b=8; c=32/3; d=4;

m1=1 m2=m1/2 m1=1; m2=m1/2; x=m1(w) (w); y=m2(w)(w);

F=matrix([[1,a,b,c],[0,1,d,b],[0,0,1,a],[0,0,0,1]]) M1=matrix([[1,0,0,0],[0,1,0,0],[0,0,1,0],[x,0,0,1]]) M2=matrix([[1,0,0,0],[0,1,0,0],[0,0,1,0],[y,0,0,1]]) F=matrix([[1,a,b,c],[0,1,d,b],[0,0,1,a],[0,0,0,1]]); M1=matrix([[1,0,0,0],[0,1,0,0],[0,0,1,0],[x,0,0,1]]); M2=matrix([[1,0,0,0],[0,1,0,0],[0,0,1,0],[y,0,0,1]]); ([[e,f,g,h],[i,j,k,l],[m,n,o,p],[q,r,s,t]])=FM1FM1FM1F*M2 A=matrix([[o,p],[s,t]]) B=A.determinant() C=solve(B==0,w) F*M2; A=matrix([[o,p],[s,t]]); B=A.determinant(); C=solve(B==0,w); numerical_approx(C)

Sagemath returns an error since there are complex numbers.

I require numerical solutions.

apologies if the question is unclear, I have zero programming background, this is for my engineering dissertation.

Any help is appreciated.

I am attempting to evaluate a matrix multiplication, then extract 4 specific cells from the resultant matrix and create a new 2x2 matrix with these 4 specific cells. I then need to calculate the points at which the determinant of the 2x2 matrix equals zero. This is to solve the resonant frequency of transverse vibration of a beam. My attempt at doing this:

e,f,g,h,i,j,k,l,m,n,o,p,g,r,s,t=var('e,f,g,h,i,j,k,l,m,n,o,p,g,r,s,t');
var("w", domain="complex");
a=4;
b=8;
c=32/3;
d=4;
d=4;
  
m1=1;
m2=m1/2;
x=m1(w);
y=m2(w);x=m1*(w);
y=m2*(w);
  
F=matrix([[1,a,b,c],[0,1,d,b],[0,0,1,a],[0,0,0,1]]);
M1=matrix([[1,0,0,0],[0,1,0,0],[0,0,1,0],[x,0,0,1]]);
M2=matrix([[1,0,0,0],[0,1,0,0],[0,0,1,0],[y,0,0,1]]);
([[e,f,g,h],[i,j,k,l],[m,n,o,p],[q,r,s,t]])=FM1FM1FM1F*M2;
([[e,f,g,h],[i,j,k,l],[m,n,o,p],[q,r,s,t]])=F*M1*F*M1*F*M1*F*M2;
A=matrix([[o,p],[s,t]]);
B=A.determinant();
C=solve(B==0,w);
numerical_approx(C)numerical_approx(C)

I am attempting to evaluate a matrix multiplication, then extract 4 specific cells from the resultant matrix and create a new 2x2 matrix with these 4 specific cells. I then need to calculate the points at which the determinant of the 2x2 matrix equals zero. This is to solve the resonant frequency of transverse vibration of a beam. My attempt at doing this:

e,f,g,h,i,j,k,l,m,n,o,p,g,r,s,t=var('e,f,g,h,i,j,k,l,m,n,o,p,g,r,s,t');
var("w", domain="complex");
a=4;
b=8;
c=32/3;
d=4;

m1=1;
m2=m1/2;
x=m1*(w);
y=m2*(w);

F=matrix([[1,a,b,c],[0,1,d,b],[0,0,1,a],[0,0,0,1]]);
M1=matrix([[1,0,0,0],[0,1,0,0],[0,0,1,0],[x,0,0,1]]);
M2=matrix([[1,0,0,0],[0,1,0,0],[0,0,1,0],[y,0,0,1]]);
([[e,f,g,h],[i,j,k,l],[m,n,o,p],[q,r,s,t]])=F*M1*F*M1*F*M1*F*M2;
A=matrix([[o,p],[s,t]]);
B=A.determinant();
C=solve(B==0,w);
numerical_approx(C)

Sagemath returns an error since there are complex numbers.

I require numerical solutions.

apologies if the question is unclear, I have zero programming background, this is for my engineering dissertation.

Any help is appreciated.

I am attempting to evaluate a matrix multiplication, then extract 4 specific cells from the resultant matrix and create a new 2x2 matrix with these 4 specific cells. I then need to calculate the points at which the determinant of the 2x2 matrix equals zero. This is to solve the resonant frequency of transverse vibration of a beam. My attempt at doing this:

e,f,g,h,i,j,k,l,m,n,o,p,g,r,s,t=var('e,f,g,h,i,j,k,l,m,n,o,p,g,r,s,t');
var("w", domain="complex");
a=4;
b=8;
c=32/3;
d=4;

m1=1;
m2=m1/2;
x=m1*(w);
y=m2*(w);

F=matrix([[1,a,b,c],[0,1,d,b],[0,0,1,a],[0,0,0,1]]);
M1=matrix([[1,0,0,0],[0,1,0,0],[0,0,1,0],[x,0,0,1]]);
M2=matrix([[1,0,0,0],[0,1,0,0],[0,0,1,0],[y,0,0,1]]);
([[e,f,g,h],[i,j,k,l],[m,n,o,p],[q,r,s,t]])=F*M1*F*M1*F*M1*F*M2;
A=matrix([[o,p],[s,t]]);
B=A.determinant();
C=solve(B==0,w);
numerical_approx(C)

Sagemath returns an error since there are complex numbers.

I require numerical solutions.

apologies if the question is unclear, I have zero programming background, this is for my engineering dissertation.

Any help is appreciated.

I am attempting to evaluate a matrix multiplication, then extract 4 specific cells from the resultant matrix and create a new 2x2 matrix with these 4 specific cells. I then need to calculate the points at which the determinant of the 2x2 matrix equals zero. This is to solve the resonant frequency of transverse vibration of a beam. My attempt at doing this:

e,f,g,h,i,j,k,l,m,n,o,p,g,r,s,t=var('e,f,g,h,i,j,k,l,m,n,o,p,g,r,s,t');
var("w", domain="complex");
a=4;
b=8;
c=32/3;
d=4;

m1=1;
m2=m1/2;
x=m1*(w);
y=m2*(w);

F=matrix([[1,a,b,c],[0,1,d,b],[0,0,1,a],[0,0,0,1]]);
M1=matrix([[1,0,0,0],[0,1,0,0],[0,0,1,0],[x,0,0,1]]);
M2=matrix([[1,0,0,0],[0,1,0,0],[0,0,1,0],[y,0,0,1]]);
([[e,f,g,h],[i,j,k,l],[m,n,o,p],[q,r,s,t]])=F*M1*F*M1*F*M1*F*M2;
A=matrix([[o,p],[s,t]]);
B=A.determinant();
C=solve(B==0,w);
numerical_approx(C)

Sagemath returns an error since there are complex numbers.

I require numerical solutions.

apologies if the question is unclear, I have zero programming background, this is for my engineering dissertation.

Any help is appreciated.