If A does not have a floating-point data type, then the Rank(A) command computes the rank of A by performing Gaussian elimination on the rows of A.

The rank of Matrix A is the number of nonzero rows in the resulting Matrix.

If Matrix A has a floating-point data type, a singular value decomposition and analysis is performed.

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

$A≔⟨⟨-7\,1\,2⟩\left|⟨2\,1\,-1⟩\right|⟨3\,0\,-1⟩|⟨2\,7\,-3⟩⟩$

$A≔\left[\begin{array}{cccc}\mathrm{-7}& 2& 3& 2\\ 1& 1& 0& 7\\ 2& \mathrm{-1}& \mathrm{-1}& \mathrm{-3}\end{array}\right]$

$\mathrm{Rank}\left(A\right)$

$2$

$\mathrm{numelems}\left(\mathrm{RowSpace}\left(A\right)\right)$

$2$