Solves the general linear system Ax = b.  For over determined systems (A has more rows than columns), the system is solved in the least squares sense.  LSolve uses LU decomposition for a square matrix; QR otherwise.

Syntax

x = LSolve(A,b)

Arguments

Name

Description

A

A matrix of real values.  Number of rows must be equal or greater than number of columns.

b

The right-hand side column vector or a matrix.  If it is a matrix, each column is considered a separate vector and the system is solved separately for each, resulting in multiple solutions.  The number of rows must be equal to the number of rows of matrix A.

Output

Name

Description

x

The solution(s) to the system(s).  It will have the same dimension as the right-hand side argument b.  Each column will be a solution corresponding to the equivalent column in b.

Example 1

Solve a pair of linear systems Ax=b for the same matrix A.

Syntax

A = [1,2,3;41,15,6;17,8,9];// square matrix A

b = [11,21;13,33;21,24]; // Two columns(i.e. 2 rhs)

x = LSolve(A,b); // Solve for each right hand side

Result

Each column is a solution for the corresponding right hand side.

x = -1.5     -5.4079

    4.5     18.355

    1.1667  -3.4342

Example 2

Find the best fit solution to the system

y = 0

3x - y = 0

3x + y = 6

Syntax

A = [0, 1; 3, -1; 3, 1]

b = [0; 0; 6]

x = LSolve(A, b)

Result

A least squares solution to the system.

x = 1

   2

See Also:

Backslash Operator