Convert linear equations to matrix form
Convert a system of linear equations to matrix form.
equationsToMatrix automatically detects the variables in the
equations by using
symvar. The returned coefficient matrix follows
the variable order determined by
syms x y z eqns = [x+y-2*z == 0, x+y+z == 1, 2*y-z == -5]; [A,b] = equationsToMatrix(eqns) vars = symvar(eqns)
A = [ 1, 1, -2] [ 1, 1, 1] [ 0, 2, -1] b = 0 1 -5 vars = [ x, y, z]
You can change the arrangement of the coefficient matrix by specifying other variable order.
vars = [x, z, y]; [A,b] = equationsToMatrix(eqns,vars)
A = [ 1, -2, 1] [ 1, 1, 1] [ 0, -1, 2] b = 0 1 -5
Convert a linear system of equations to the matrix form by specifying independent variables. This is useful when the equation are only linear in some variables.
For this system, specify the variables as
[s t] because the
system is not linear in
syms r s t eqns = [s-2*t+r^2 == -1 3*s-t == 10]; vars = [s t]; [A,b] = equationsToMatrix(eqns,vars)
A = [ 1, -2] [ 3, -1] b = - r^2 - 1 10
Return only the coefficient matrix of the equations by specifying a single output argument.
syms x y z eqns = [x+y-2*z == 0, x+y+z == 1, 2*y-z == -5]; vars = [x y z]; A = equationsToMatrix(eqns,vars)
A = [ 1, 1, -2] [ 1, 1, 1] [ 0, 2, -1]
eqns— Linear equations
Linear equations, specified as a vector of symbolic equations or expressions.
Symbolic equations are defined by using the
== operator, such as
x + y == 1. For symbolic expressions,
equationsToMatrix assumes that the right side is 0.
Equations must be linear in terms of
A— Coefficient matrix
Coefficient matrix of the system of linear equations, specified as a symbolic matrix.
b— Right sides of equations
Vector containing the right sides of equations, specified as a symbolic matrix.
A system of linear equations
can be represented as the matrix equation . Here, A is the coefficient matrix.
is the vector containing the right sides of equations.