For Matrix A and Vector B, the LeastSquares(A, B) command returns a Vector that best satisfies the condition $A·x$ is approximately equal to B, in the least squares sense. The result that is returned is the Vector x which minimizes Norm(A . x - B, 2).

Parameter A can also be a set of equations that describe the linear least squares problem. In this case, B is the set of variables in which the equations in A occur.

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{LinearAlgebra}\right]\right)\:$

$A≔⟨⟨3\,0\,4⟩|⟨-2\,3\,4⟩⟩\:$

$b≔⟨1\,2\,4⟩\:$

$X≔\mathrm{LeastSquares}\left(A\,b\right)$

$X≔\left[\begin{array}{c}\frac{351}{625}\\ \frac{62}{125}\end{array}\right]$

$\mathrm{Norm}\left(A·X-b\right)$

$\frac{16}{25}$

$E≔\left\{2x-y+2=0\,mx+ny-3=0\right\}\:$

$V≔\left\{x\,y\right\}\:$

$\mathrm{LeastSquares}\left(E\,V\right)$

$\left\{x=-\frac{2n-3}{m+2n}\,y=\frac{2\left(m+3\right)}{m+2n}\right\}$