Convert set of linear equations to matrix form
[A,b] =
equationsToMatrix(eqns,vars)
[A,b] =
equationsToMatrix(eqns)
A = equationsToMatrix(eqns,vars)
A = equationsToMatrix(eqns)
[
converts A
,b
] =
equationsToMatrix(eqns
,vars
)eqns
to
the matrix form. Here eqns
must be linear equations
in vars
.
[
converts A
,b
] =
equationsToMatrix(eqns
)eqns
to
the matrix form. Here eqns
must be a linear system
of equations in all variables that symvar
finds
in these equations.
converts A
= equationsToMatrix(eqns
,vars
)eqns
to
the matrix form and returns only the coefficient matrix. Here eqns
must
be linear equations in vars
.
converts A
= equationsToMatrix(eqns
)eqns
to
the matrix form and returns only the coefficient matrix. Here eqns
must
be a linear system of equations in all variables that symvar
finds
in these equations.

Vector of equations or equations separated by commas. Each equation
is either a symbolic equation defined by the relation operator Equations must be linear in terms of 

Independent variables of Default: Variables determined by 

Coefficient matrix of the system of linear equations. 

Vector containing the right sides of equations. 
Convert this system of linear equations to the matrix form. To get the coefficient matrix and the vector of the right sides of equations, assign the result to a vector of two output arguments:
syms x y z [A, b] = equationsToMatrix([x + y  2*z == 0, x + y + z == 1,... 2*y  z + 5 == 0], [x, y, z])
A = [ 1, 1, 2] [ 1, 1, 1] [ 0, 2, 1] b = 0 1 5
Convert this system of linear equations to the matrix form.
Assigning the result of the equationsToMatrix
call
to a single output argument, you get the coefficient matrix. In this
case, equationsToMatrix
does not return the vector
containing the right sides of equations:
syms x y z A = equationsToMatrix([x + y  2*z == 0, x + y + z == 1,... 2*y  z + 5 == 0], [x, y, z])
A = [ 1, 1, 2] [ 1, 1, 1] [ 0, 2, 1]
Convert this linear system of equations to the matrix form without
specifying independent variables. The toolbox uses symvar
to
identify variables:
syms s t [A, b] = equationsToMatrix([s  2*t + 1 == 0, 3*s  t == 10])
A = [ 1, 2] [ 3, 1] b = 1 10
Find the vector of variables determined for this system by symvar
:
X = symvar([s  2*t + 1 == 0, 3*s  t == 10])
X = [ s, t]
Convert X
to a column vector:
X = X.'
X = s t
Verify that A
, b
, and X
form
the original equations:
A*X == b
ans = s  2*t == 1 3*s  t == 10
If the system is only linear in some variables, specify those variables explicitly:
syms a s t [A, b] = equationsToMatrix([s  2*t + a == 0, 3*s  a*t == 10], [t, s])
A = [ 2, 1] [ a, 3] b = a 10
You also can specify equations and variables all together, without using vectors and simply separating each equation or variable by a comma. Specify all equations first, and then specify variables:
syms x y [A, b] = equationsToMatrix(x + y == 1, x  y + 1, x, y)
A = [ 1, 1] [ 1, 1] b = 1 1
Now change the order of the input arguments as follows. equationsToMatrix
finds
the variable y
, then it finds the expression x
— y + 1
. After that, it assumes that all remaining
arguments are equations, and stops looking for variables. Thus, equationsToMatrix
finds
the variable y
and the system of equations x
+ y = 1, x = 0, x  y + 1 = 0
:
[A, b] = equationsToMatrix(x + y == 1, x, x  y + 1, y)
A = 1 0 1 b = 1  x x  x  1
If you try to convert a nonlinear system of equations, equationsToMatrix
throws
an error:
syms x y [A, b] = equationsToMatrix(x^2 + y^2 == 1, x  y + 1, x, y)
Error using symengine (line 56) Cannot convert to matrix form because the system does not seem to be linear.
linsolve
 odeToVectorField
 solve
 symvar