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The rank of a matrix (sometimes noted as Rk) is mainly defined as the maximum number of row vectors (or column vectors) which are linearly independent.

The rank of a matrix is also the dimension of the vector subspace created by the vectors (either rows or columns) of the matrix.

The rank can be calculated for both rows and columns, it will be the same value.

How to calculate a matrix rank?

To calculate the rank of a $ M $ matrix, compare each of the rows between them and each of the columns between them to verify that they are two-by-two linearly independent.

Example: $$ M = \begin{bmatrix} 1 & 2 & 3 \\ 2 & 4 & 6 \\ 2 & 2 & 4 \end{bmatrix} $$ The matrix $ M $ has rank $ 2 $ because line 2 is twice the line 1, they are not linearly independent. NB: column 3 is the sum of columns 1 and 2, they are not linearly independent.

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