Method on @sym: mldivide (A, b) ¶

Operator on @sym: A \ b ¶

Symbolic backslash: solve symbolic linear systems.

This operator tries to broadly match the behaviour of the backslash operator for double matrices. For scalars, this is just division:

sym(2) \ 1
  ⇒ ans = (sym) 1/2

But for matrices, it solves linear systems

A = sym([1 2; 3 4]);
b = sym([5; 11]);
x = A \ b
  ⇒ x = (sym 2×1 matrix)
      ⎡1⎤
      ⎢ ⎥
      ⎣2⎦
A*x == b
  ⇒ ans = (sym 2×1 matrix)
      ⎡True⎤
      ⎢    ⎥
      ⎣True⎦

Over- and under-determined systems are supported:

A = sym([5 2]);
x = A \ 10
  ⇒ x = (sym 2×1 matrix)
      ⎡    2⋅c₁⎤
      ⎢2 - ────⎥
      ⎢     5  ⎥
      ⎢        ⎥
      ⎣   c₁   ⎦
A*x == 10
  ⇒ ans = (sym) True

A = sym([1 2; 3 4; 9 12]);
b = sym([5; 11; 33]);
x = A \ b
  ⇒ x = (sym 2×1 matrix)
      ⎡1⎤
      ⎢ ⎥
      ⎣2⎦
A*x - b
  ⇒ ans = (sym 3×1 matrix)
      ⎡0⎤
      ⎢ ⎥
      ⎢0⎥
      ⎢ ⎥
      ⎣0⎦

See also: @sym/ldivide, @sym/mrdivide.

Package: symbolic