Convert linear equations to matrix form
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)
You can change the arrangement of the coefficient matrix by specifying other variable order.
vars = [x,z,y]; [A,b] = equationsToMatrix(eqns,vars)
Specify Variables in Equations
Convert a linear system of equations to the matrix form by specifying independent variables. This is useful when the equations 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)
Return Only Coefficient Matrix of Equations
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)
Solve System of Equations That Are Functions of Time
Consider the following system of linear equations that are functions of time:
Declare the system of equations.
syms x(t) y(t) z(t) u(t) v(t) eqn1 = 2*x + y + z == 2*u; eqn2 = -x + y - z == v; eqn3 = x + 2*y + 3*z == -10; eqn = [eqn1; eqn2; eqn3]
Specify the independent variables , , and in the equations as a symbolic vector
vars. Use the
equationsToMatrix function to convert the system of equations into the matrix form.
vars = [x(t); y(t); z(t)]; [A,b] = equationsToMatrix(eqn,vars)
Solve the matrix form of the equations using the
X = linsolve(A,b)
Evaluate the solution for the functions and . Plot the solution.
zSol = subs(X(3),[u(t) v(t)],[cos(t) sin(2*t)])
eqns — Linear equations
vector of symbolic equations or expressions
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.
Matrix Representation of System of Linear Equations
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.