If A is a square, nonsingular matrix, then the solution of the equation Ax=b is . Matlab implements this operation with the backslash operator:
>> A = rand(3,3) A = 0.2190 0.6793 0.5194 0.0470 0.9347 0.8310 0.6789 0.3835 0.0346 >> b = rand(3,1) b = 0.0535 0.5297 0.6711 >> x = A\b x = -159.3380 314.8625 -344.5078 >> A*x-b ans = 1.0e-13 * -0.2602 -0.1732 -0.0322(Notice the use of the built-in function rand, which creates a matrix with entries from a uniform distribution on the interval (0,1). See help rand for more details.) Thus
A\bis (mathematically) equivalent to multiplying b on the left by (however, Matlab does not compute the inverse matrix; instead it solves the linear system directly). When used with a nonsquare matrix, the backslash operator solves the appropriate system in the least-squares sense; see help slash for details. Of course, as with the other arithmetic operators, the matrices must be compatible in size. The division operator is not defined for n-dimensional arrays with n>2.