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The function rank(A) computes the rank of a matrix by performing Gaussian elimination on the rows of the given matrix. The rank of the matrix A is the number of non-zero rows in the resulting matrix.

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

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

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

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

$2$