How can I solve A*X + X*B = C equation for X? where A, B&C are 2*2 matrixes.
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A = [1 1;2 3] B= [5 6;7 8] C = [11 12;13 14] Syms X; Eqn = A*X + X*B == C; solve(Eqn,X); % I'm facing difficulties to define matrix X as syms
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Andrei Bobrov
on 1 Jun 2017
>> A = [1 1;2 3];
B= [5 6;7 8];
C = [11 12;13 14];
X = reshape(sym('x',[4,1],'real'),2,[]);
v = A*X + X*B - C;
v = v(:);
f = matlabFunction(v,'Vars',{X});
x = fsolve(f,[1;1;1;1])
Equation solved.
fsolve completed because the vector of function values is near zero
as measured by the default value of the function tolerance, and
the problem appears regular as measured by the gradient.
<stopping criteria details>
x =
2.1809
-0.1489
-0.2766
1.4043
>> X = reshape(x,2,[]);
>> v = A*X + X*B - C
v =
1.0e-14 *
-0.3553 -0.3553
-0.1776 -0.5329
>>
5 Comments
Andrei Bobrov
on 1 Jun 2017
Edited: Andrei Bobrov
on 1 Jun 2017
Same
>> A = [1 1;2 3] ;
B= [5 6;7 8] ;
C = [11 12;13 14] ;
syms x1 y1 x2 y2
X = [x1 y1 ; x2 y2] ;
eqn = A*X+X*B == C ;
D = solve(eqn);
X = reshape(sym('x',[4,1],'real'),2,[]);
v = A*X + X*B - C;
v = v(:);
f = matlabFunction(v,'Vars',{X});
x = fsolve(f,[1;1;1;1]);
Equation solved.
fsolve completed because the vector of function values is near zero
as measured by the default value of the function tolerance, and
the problem appears regular as measured by the gradient.
<stopping criteria details>
>> structfun(@double,D) - x
ans =
1.0e-14 *
0.6217
-0.4469
-0.4219
0.3775
>>
Karan Gill
on 5 Jun 2017
You can solve this with the symbolic toolbox if you declare "X" as a matrix:
>> X = sym('x%d',[2 2])
X =
[ x11, x12]
[ x21, x22]
Then solve as usual:
>> A = [1 1;2 3];
B= [5 6;7 8];
C = [11 12;13 14];
>> eqn = A*X + X*B == C
eqn =
[ 6*x11 + 7*x12 + x21 == 11, 6*x11 + 9*x12 + x22 == 12]
[ 2*x11 + 8*x21 + 7*x22 == 13, 2*x12 + 6*x21 + 11*x22 == 14]
>> sol = solve(eqn,X)
sol =
struct with fields:
x11: [1×1 sym]
x21: [1×1 sym]
x12: [1×1 sym]
x22: [1×1 sym]
>> solX = [sol.x11 sol.x12; sol.x21 sol.x22]
solX =
[ 205/94, -13/47]
[ -7/47, 66/47]
>> vpa(solX)
ans =
[ 2.1808510638297872340425531914894, -0.27659574468085106382978723404255]
[ -0.1489361702127659574468085106383, 1.4042553191489361702127659574468]
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