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Solve systems of linear equations *Ax = B* for *x*

`x = A\B`

`x = mldivide(A,B)`

solves
the system of linear equations `x`

= `A`

\`B`

`A*x = B`

. The matrices `A`

and `B`

must
have the same number of rows. MATLAB^{®} displays a warning message
if `A`

is badly scaled or nearly singular, but
performs the calculation regardless.

If

`A`

is a scalar, then`A\B`

is equivalent to`A.\B`

.If

`A`

is a square`n`

-by-`n`

matrix and`B`

is a matrix with`n`

rows, then`x = A\B`

is a solution to the equation`A*x = B`

, if it exists.If

`A`

is a rectangular`m`

-by-`n`

matrix with`m ~= n`

, and`B`

is a matrix with`m`

rows, then`A`

\`B`

returns a least-squares solution to the system of equations`A*x= B`

.

If

`A`

is a square matrix,`A`

\`B`

is roughly equal to`inv(A)*B`

, but MATLAB processes`A`

\`B`

differently and more robustly.If the rank of

`A`

is less than the number of columns in`A`

, then`x`

=`A`

\`B`

is not necessarily the minimum norm solution. The more computationally expensive`x = pinv(A)*B`

computes the minimum norm least-squares solution.For full singular inputs, you can compute the least-squares solution using the function

`linsolve`

.

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