If A is a square matrix and B is a matrix, then mldivide(A,B) computes X, where X is the solution to the matrix equation A * X=B.

If A is a non-square matrix and B is a matrix, then mldivide(A,B) computes X, where X is a solution to the linear system A * X=B, in the least squares sense.

Maple normally treats arrays and vectors as distinct from matrices, in some cases not permitting a matrix operation when the given argument is not specifically declared as a matrix.  This function implicitly extends arrays and vectors to 2 dimensions.  Notably, n-element column vectors are treated as n x 1 matrices.  Also, n-element row vectors and 1-D arrays are treated as 1 x n matrices.

If A is a scalar, then mldivide(A,B) computes ldivide(A,B).

If B is a scalar, then mldivide(A,B)  is computed as if B is a 1 x 1 matrix.

$\mathrm{with}\left(\mathrm{MTM}\right)\:$

$A≔\mathrm{Matrix}\left(\left[\left[1\,2\,1\right]\,\left[4\,5\,6\right]\,\left[2\,8\,1\right]\right]\right)$

$A≔\left[\begin{array}{ccc}1& 2& 1\\ 4& 5& 6\\ 2& 8& 1\end{array}\right]$

$B≔\mathrm{Vector}\left[\mathrm{column}\right]\left(\left[8\,32\,21\right]\right)$

$B≔\left[\begin{array}{c}8\\ 32\\ 21\end{array}\right]$

$\mathrm{mldivide}\left(A\,B\right)$

$\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right]$

$A≔\mathrm{Matrix}\left(\left[\left[1\,2\,1\right]\,\left[4\,5\,6\right]\,\left[2\,8\,1\right]\right]\right)$

$A≔\left[\begin{array}{ccc}1& 2& 1\\ 4& 5& 6\\ 2& 8& 1\end{array}\right]$

$B≔\mathrm{Matrix}\left(\left[\left[8\,20\,32\right]\,\left[32\,77\,122\right]\,\left[21\,54\,87\right]\right]\right)$

$B≔\left[\begin{array}{ccc}8& 20& 32\\ 32& 77& 122\\ 21& 54& 87\end{array}\right]$

$\mathrm{mldivide}\left(A\,B\right)$

$\left[\begin{array}{ccc}1& 4& 7\\ 2& 5& 8\\ 3& 6& 9\end{array}\right]$

$A≔\mathrm{Matrix}\left(\left[\left[1\,2\,1\right]\,\left[4\,5\,6\right]\right]\right)$

$A≔\left[\begin{array}{ccc}1& 2& 1\\ 4& 5& 6\end{array}\right]$

$B≔\mathrm{Vector}\left[\mathrm{column}\right]\left(\left[8\,32\right]\right)$

$B≔\left[\begin{array}{c}8\\ 32\end{array}\right]$

$\mathrm{mldivide}\left(A\,B\right)$

$\left[\begin{array}{c}\frac{52}{31}\\ \frac{56}{31}\\ \frac{84}{31}\end{array}\right]$

$A≔\mathrm{Matrix}\left(\left[\left[1\,2\,1\right]\,\left[4\,5\,6\right]\right]\right)$

$A≔\left[\begin{array}{ccc}1& 2& 1\\ 4& 5& 6\end{array}\right]$

$B≔\mathrm{Matrix}\left(\left[\left[8\,20\,32\right]\,\left[32\,77\,122\right]\right]\right)$

$B≔\left[\begin{array}{ccc}8& 20& 32\\ 32& 77& 122\end{array}\right]$

$\mathrm{mldivide}\left(A\,B\right)$

$\left[\begin{array}{ccc}\frac{52}{31}& 4& \frac{196}{31}\\ \frac{56}{31}& 5& \frac{254}{31}\\ \frac{84}{31}& 6& \frac{288}{31}\end{array}\right]$