MATLAB: Rewrite A=[3*1] matrix to [3*3]*[3*1(var)]=A

syms factor

dear all
i have 3*1 matrix like matrix E below
syms qd td ed q teta
E =[ ed*cos(q)*sin(teta) - cos(teta)*(qd*cos(q)*sin(teta) + td*cos(teta)*sin(q)) - td*sin(q)*sin(teta)^2 ; cos(teta)*(td*cos(teta)*sin(q) - qd*sin(q)*sin(teta)) + ed*sin(q)*sin(teta) + td*cos(q)*sin(teta)^2  ;  ed*cos(teta) + cos(q)*sin(teta)*(qd*cos(q)*sin(teta) + td*cos(teta)*sin(q)) - sin(q)*sin(teta)*(td*cos(teta)*sin(q) - qd*sin(q)*sin(teta))]
that i want to rewrite it in [3*3]*[qd;td;ed]=[E] this form
is there any Command that can help me to calculate this [3*3] matrix by matlab
answer should be like this:
[                 -cos(q)*cos(teta)*sin(teta),                        - cos(teta)^2*sin(q) - sin(q)*sin(teta)^2, cos(q)*sin(teta)]
[                 -cos(teta)*sin(q)*sin(teta),                          sin(q)*cos(teta)^2 + cos(q)*sin(teta)^2, sin(q)*sin(teta)]
[ cos(q)^2*sin(teta)^2 + sin(q)^2*sin(teta)^2, cos(q)*cos(teta)*sin(q)*sin(teta) - cos(teta)*sin(q)^2*sin(teta),        cos(teta)]
i really apreciated if you could help me

Best Answer

Doing it by matrix division (the mldivide function) did not work because the rows are not consistent.
The only solution I can come up with is:
syms qd td ed q teta
E =[ ed*cos(q)*sin(teta) - cos(teta)*(qd*cos(q)*sin(teta) + td*cos(teta)*sin(q)) - td*sin(q)*sin(teta)^2 ; cos(teta)*(td*cos(teta)*sin(q) - qd*sin(q)*sin(teta)) + ed*sin(q)*sin(teta) + td*cos(q)*sin(teta)^2  ;  ed*cos(teta) + cos(q)*sin(teta)*(qd*cos(q)*sin(teta) + td*cos(teta)*sin(q)) - sin(q)*sin(teta)*(td*cos(teta)*sin(q) - qd*sin(q)*sin(teta))];
v = [qd;td;ed];
for k1 = 1:size(E,1)
    C{k1} = coeffs(E(k1), v);
end
Out = [C{1}; C{2}; C{3}]
The columns of ‘Out’ are with respect to the elements of ‘v’, in order. Change the order of ‘v’ to produce the result you want.
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