# ldivide, .\

Symbolic array left division

## Syntax

B.\A
ldivide(B,A)

## Description

example

B.\A divides A by B.
ldivide(B,A) is equivalent to B.\A.

## Examples

### Divide Scalar by Matrix

Create a 2-by-3 matrix.

B = sym('b', [2 3])
B = [ b1_1, b1_2, b1_3] [ b2_1, b2_2, b2_3]

Divide the symbolic expression sin(a) by each element of the matrix B.

syms a B.\sin(a)
ans = [ sin(a)/b1_1, sin(a)/b1_2, sin(a)/b1_3] [ sin(a)/b2_1, sin(a)/b2_2, sin(a)/b2_3]

### Divide Matrix by Matrix

Create a 3-by-3 symbolic Hilbert matrix and a 3-by-3 diagonal matrix.

H = sym(hilb(3)) d = diag(sym([1 2 3]))
H = [ 1, 1/2, 1/3] [ 1/2, 1/3, 1/4] [ 1/3, 1/4, 1/5] d = [ 1, 0, 0] [ 0, 2, 0] [ 0, 0, 3]

Divide d by H by using the elementwise left division operator .\. This operator divides each element of the first matrix by the corresponding element of the second matrix. The dimensions of the matrices must be the same.

H.\d
ans = [ 1, 0, 0] [ 0, 6, 0] [ 0, 0, 15]

### Divide Expression by Symbolic Function

Divide a symbolic expression by a symbolic function. The result is a symbolic function.

syms f(x) f(x) = x^2; f1 = f.\(x^2 + 5*x + 6)
f1(x) = (x^2 + 5*x + 6)/x^2

## Input Arguments

collapse all

Input, specified as a symbolic variable, vector, matrix, multidimensional array, function, or expression. Inputs A and B must be the same size unless one is a scalar. A scalar value expands into an array of the same size as the other input.

Input, specified as a symbolic variable, vector, matrix, multidimensional array, function, or expression. Inputs A and B must be the same size unless one is a scalar. A scalar value expands into an array of the same size as the other input.