Untitled

For a square matrix

, the command A\b is mathematically equivalent to

A = magic(3)
A = 
     8     1     6
     3     5     7
     4     9     2
b = [1;2;3];
x = A\b
x = 
   0.050000000000000
   0.300000000000000
   0.050000000000000

One way to check the answer is to compute a quantity known as the residual. It is (hopefully) close to machine precision, scaled by the size of the entries of the data.

residual = b - A*x
residual = 
     0
     0
     0

If the matrix is singular, a warning is produced, but you get an answer anyway.

A = [0 1; 0 0];   % known to be singular
b = [1;2];
x = A\b
Warning: Matrix is singular to working precision.
x = 
  -Inf
   Inf

When you get a warning, it's important to check the result rather than blindly accepting it as correct.