Rank in matrices

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I have been told multiple things and just want to clear it up, To find the rank of a matrix, is it just the number of leading entries when row reduced?

What does this mean?

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If you think of matrices as functions between vector spaces, then the rank is the dimension of the range of the function.

But yes, a way to compute it is by counting the numbers of nonzero pivots in reduced row echelon form. This is because for every row of the matrix with a pivot, there is a vector in the range with a non-zero component in that row.