`mldivide`

Left matrix division, the backslash operator, for solving linear systems.

Syntax

x = A\b

Solves A*x = b.

x = mldivide(A, b)

Function form of A\b.

Description

The backslash chooses a method from the shape of A: for a square matrix an LU factorization (a triangular solve if A is triangular, Cholesky if it is symmetric positive definite); for a non-square matrix a least-squares solution via QR.

It is the recommended way to solve systems, preferable to inv(A)*b. For several right-hand sides, pass them as columns of b in a single call.

Input arguments

A: Coefficient matrix. Square for an exact solve; rectangular for least squares.
b: Right-hand side with size(A,1) rows. A scalar A divides every element of b.

Output arguments

x: The solution with size(A,2) rows.

Example

Square, overdetermined and scalar cases

[2 1; 1 3] \ [3; 5]
[1 2; 3 4; 5 6] \ [1; 2; 3]
2 \ 6

Output

ans = 2×1

    0.8000
    1.4000
ans = 2×1

         0
    0.5000
ans = 3

mldivide