how I solve it in MATLAB software?
Answers
Solve System of Linear Equations Using linsolve
A system of linear equations
a
11
x
1
+a
12
x
2
+…+a
1n
x
n
=b
1
a
21
x
1
+a
22
x
2
+…+a
2n
x
n
=b
2
⋯
a
m1
x
1
+a
m2
x
2
+…+a
mn
x
n
=b
m
can be represented as the matrix equation A⋅
→
x
=
→
b
, where A is the coefficient matrix,
A=
a
11
⋮
a
m1
…
⋱
⋯
a
1n
⋮
a
mn
and
→
b
is the vector containing the right sides of equations,
→
b
=
b
1
⋮
b
m
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.
2x+y+z=2
−x+y−z=3
x+2y+3z=−10
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.
2x+y+z=2
−x+y−z=3
x+2y+3z=−10
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.