mrdivide - Solve systems of linear equations xA = B for

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Solve systems of linear equations xA = B for_x_

Syntax

Description

[x](#btg5p6j-x) = [B](#btg5p6j-A)/[A](#btg5p6j-A) solves the system of linear equations x*A = B forx. The matrices A andB 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 squaren-by-n matrix andB is a matrix with n columns, then x = B/A is a solution to the equationx*A = B, if it exists.
• If A is a rectangularm-by-n matrix with m ~= n, and B is a matrix withn columns, then x = B/A returns a least-squares solution of the system of equations x*A = B.

example

[x](#btg5p6j-x) = mrdivide([B](#btg5p6j-A),[A](#btg5p6j-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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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

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.

MATLAB® issues a warning but proceeds with calculation.

Verify that x is not an exact solution.

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. IfA is anm-by-n matrix andB is a p-by-n matrix, then x is ap-by-m matrix.

x is sparse only if both A andB 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

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This function supports tall arrays with the limitation:

For the syntax Z = X/Y, theY operand must be a scalar.

For more information, see Tall Arrays for Out-of-Memory Data.

Usage notes and limitations:

• Code generation does not support sparse matrix inputs for this function.
• If the code generator determines that A is a scalar at compile time, then B/A is equivalent toB./A.
  Otherwise, even if the run-time value of A is a scalar, the code generator treats A as a matrix and requires the number of columns in A andB to be equal. So, if B has more than one column, the code generator produces an error.

Usage notes and limitations:

• Code generation does not support sparse matrix inputs for this function.
• If the code generator determines that A is a scalar at compile time, then B/A is equivalent toB./A.
  Otherwise, even if the run-time value of A is a scalar, the code generator treats A as a matrix and requires the number of columns in A andB to be equal. So, if B has more than one column, the code generator produces an error.

The mrdivide function supports GPU array input with these usage notes and limitations:

• If B is rectangular, then it must also be nonsparse.
• The MATLABmrdivide function prints a warning ifB is badly scaled, nearly singular, or rank deficient. The gpuArray mrdivide is unable to check for this condition. Take action to avoid this condition.

For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Usage notes and limitations:

• If B is rectangular, then it must also be nonsparse.
• The MATLABmrdivide function prints a warning ifB is badly scaled, nearly singular, or rank deficient. The distributed array mrdivide is unable to check for this condition. Take action to avoid this condition.
• If B is an M-by-N matrix with N > M, for distributed arrays, mrdivide computes a solution that minimizesnorm(X). The result is the same as the result ofPINV(B)*A.

For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).

Version History

Introduced before R2006a