Question

This is probably very simple but I’m having trouble setting up matrices to solve two linear equations using symbolic objects.

The equations are on the form:

(1) a11*x1 + a12*x2 + b1 = 0
(2) a21*x1 + a22*x2 + b2 = 0

So I have a vector {E}:

      [ a11*x1 + a12*x2 + b1 ]
{E} = [ a21*x1 + a22*x2 + b2 ]

I want to get a matrix [A] and a vector {B} so I can solve the equations, i.e.
[A]*{X} + {B} = 0 => {X} = -[A]{B}.

Where

      [ x1 ]
{X} = [ x2 ]

      [ a11 a12 ]
[A] = [ a21 a22 ]

      [ b1 ]
{B} = [ b2 ]

Matrix [A] is just the Jacobian matrix of {E} but what operation do I have to perform on {E} to get {B}, i.e. the terms that don’t include an x?

This is what I have done:

x = sym('x', [2 1]);
a = sym('a', [2 2]);
b = sym('b', [2 1]);

E = a*x + b;
A = jacobian(E,x);

n = length(E);
B = -E;
for i = 1:n
    for j = 1:n
        B(i) = subs(B(i), x(j), 0);
    end
end

X = A\B

I’m thinking there must be some function that does this in one line.

So basically my question is: what can I do instead of those for loops?

(I realize this is something very simple and easily found by searching. The problem is I don’t know what this is called so I don’t know what to look for.)

Answer 1

It is just B = subs(B,x,[0 0])