matlab: matrix symbolic solution -

thanks time , help. actually, made mistake in previous post when specifying problem. thus, reformulate question using simpler example. need solve symbolically equation ct = z/(p-i) or ct*(p-i) = z.

i know answer => ct = [sigma, 1-sigma]

how program "correctly" code in order solution

syms sigma; ct = sym('ct',[1 2]); %     p = [sigma  1-sigma;      sigma  1-sigma]; = [1 0;      0 1]; z = [0 0]; %     solve(ct*(p-i) == z); 

so far, :

z =

0 0

warning: solutions parametrized symbols: z = c_

in solve @ 190 in test_matrix_sigma @ 13

or

  solve(ct == z/(p-i), ct); 

i get:

warning: system rank deficient. solution not unique. warning: 4 equations in 2 variables.

in /opt/matlab/r2013a/toolbox/symbolic/symbolic/symengine.p>symengine @ 56 in mupadengine.mupadengine>mupadengine.evalin @ 97 in mupadengine.mupadengine>mupadengine.feval @ 150 in solve @ 170 in test_matrix_sigma @ 13

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thanks answer !

now have 2 issues: 1) when try handla more complicated system:

syms b p1 p2; = [1 0 0 0;      0 1 0 0;      0 0 1 0;      0 0 0 1];  %     p = [a*p1     (1-a)*p1     (1-b)*(1-p1)  b*(1-p1);          a*p1     (1-a)*p1     (1-b)*(1-p1)  b*(1-p1);          b*(1-p2) (1-b)*(1-p2) (1-b)*p2      b*(1-p2);          b*(1-p2) (1-b)*(1-p2) (1-b)*p2      b*(1-p2)];     %     assume(a, 'real');  assume(b, 'real');  assume(p1, 'real');  assume(p2, 'real'); % answer = null((p-i)'); disp(answer); 

i

ans =  [ empty sym ] 

as answer.

2) if there way in maltlab "solve" above symbolic matrix p , find symbolic determinant ?

for instance, if eid(p) works;

when det(p) gives 0 answer...

this post answer different problem, first asked op before being edited. leave problem , solution here in case ever runs same problem:

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i need solve symbolically following matrix equation find out ct (a vector ???):

syms b p1 p2     %     p = [a*p1     (1-a)*p1     (1-b)*(1-p1)  b*(1-p1);          a*p1     (1-a)*p1     (1-b)*(1-p1)  b*(1-p1);          b*(1-p2) (1-b)*(1-p2) (1-b)*p2      b*(1-p2);          b*(1-p2) (1-b)*(1-p2) (1-b)*p2      b*(1-p2)];     %     solve(ct*(p-1) == 0, ct); 

how proceed ?

so far get:

undefined function or variable 'ct'.

error in matrix_test (line 10) solve(ct*(p-1) == 0, ct); 

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the error because did not assign ct before trying solve equation. in equation ct*(p-1) == 0, matlab not know ct is. remedy creating symbolic vector (see sym documentation). instance:

ct = sym('ct', [1 4]); 

however, using solve on not give solutions you're looking for: instead, matlab going give trivial answer ct = 0, of course correct answer equation.

what want find null space of (p-1)' matrix: null space set of vectors x such (p-1)'x = 0 (which same thing x'(p-1) = 0, ct = x'). matlab function null (see doc) need. using code, get:

null((p-1)')  ans =  [ -1,  0] [  1,  0] [  0, -1] [  0,  1] 

this means linear combination of vectors [-1, 1, 0, 0] , [0, 0, -1, 1] belong null space of (p-1)', , therefore transpose ct looking for.

n.b.: result confirmed observation of initial matrix p.