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Solve System of Linear Equations Using linsolve

A system of linear equations

can be represented as the matrix equation $$A\cdot \overrightarrow{x}=\overrightarrow{b}$$, where A is the coefficient matrix,

and $$\overrightarrow{b}$$ is the vector containing the right sides of equations,

If you do not have the system of linear equations in the form AX = B, use equationsToMatrix to convert the equations into this form. Consider the following system.

Declare the system of equations.

syms x y z
eqn1 = 2*x + y + z == 2;
eqn2 = -x + y - z == 3;
eqn3 = x + 2*y + 3*z == -10;

Use equationsToMatrix to convert the equations into the form AX = B. The second input to equationsToMatrix specifies the independent variables in the equations.

[A,B] = equationsToMatrix([eqn1, eqn2, eqn3], [x, y, z])

A =
[  2, 1,  1]
[ -1, 1, -1]
[  1, 2,  3]
 
B =
   2
   3
 -10

Use linsolve to solve AX = B for the vector of unknowns X.

X = linsolve(A,B)

X =
  3
  1
 -5

From X, x = 3, y = 1 and z = -5.

Solve System of Linear Equations Using solve

Use solve instead of linsolve if you have the equations in the form of expressions and not a matrix of coefficients. Consider the same system of linear equations.

Declare the system of equations.

syms x y z
eqn1 = 2*x + y + z == 2;
eqn2 = -x + y - z == 3;
eqn3 = x + 2*y + 3*z == -10;

Solve the system of equations using solve. The inputs to solve are a vector of equations, and a vector of variables to solve the equations for.

sol = solve([eqn1, eqn2, eqn3], [x, y, z]);
xSol = sol.x
ySol = sol.y
zSol = sol.z

xSol =
3
ySol =
1
zSol =
-5

solve returns the solutions in a structure array. To access the solutions, index into the array.