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mrdivide, /

Solve systems of linear equations xA = B for x

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Syntax

x = B/A
x = mrdivide(B,A)

Description

x = B/A solves the system of linear equations x*A = B for x. The matrices A and B must contain the same number of columns. MATLAB® displays a warning message if A is badly scaled or nearly singular, but performs the calculation regardless.

  • If A is a scalar, then B/A is equivalent to B./A.

  • If A is a square n-by-n matrix and B is a matrix with n columns, then x = B/A is a solution to the equation x*A = B, if it exists.

  • If A is a rectangular m-by-n matrix with m ~= n, and B is a matrix with n columns, then x = B/A returns a least-squares solution of the system of equations x*A = B.

example

x = mrdivide(B,A) is an alternative way to execute x = B/A, but is rarely used. It enables operator overloading for classes.

Examples

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Open Live Script

Solve a system of equations that has a unique solution, x*A = B. 

A = [1 1 3; 2 0 4; -1 6 -1];
B = [2 19 8];
x = B/A
x = 1×3

    1.0000    2.0000    3.0000
Open Live Script

Solve an underdetermined system, x*C = D. 

C = [1 0; 2 0; 1 0];
D = [1 2];
x = D/C
Warning: Rank deficient, rank = 1, tol =  1.332268e-15.

x = 1×3

         0    0.5000         0

MATLAB® issues a warning but proceeds with calculation.

Verify that x is not an exact solution. 

x*C-D
ans = 1×2

     0    -2

Input Arguments

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Operands, specified as vectors, full matrices, or sparse matrices. A and B must have the same number of columns.

  • If A or B has an integer data type, the other input must be scalar. Operands with an integer data type cannot be complex.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical | char
Complex Number Support: Yes

Output Arguments

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Solution, returned as a vector, full matrix, or sparse matrix. If A is an m-by-n matrix and B is a p-by-n matrix, then x is a p-by-m matrix.

x is sparse only if both A and B are sparse matrices.

Tips

  • The operators / and \ are related to each other by the equation B/A = (A'\B')'.

  • If A is a square matrix, then B/A is roughly equal to B*inv(A), but MATLAB processes B/A differently and more robustly.

  • Use decomposition objects to efficiently solve a linear system multiple times with different right-hand sides. decomposition objects are well-suited to solving problems that require repeated solutions, since the decomposition of the coefficient matrix does not need to be performed multiple times.

Extended Capabilities

Version History

Introduced before R2006a

See Also

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