So, let's say I have a 4x2 matrix with a positive rank.
The maximum rank of the matrix is 2, and if the rank of the matrix is 1 I then know that one of the lines in the matrix is a scalar times the other line of the matrix.
Now, let's say I have a 6x3 matrix with a positive rank. The maximum rank of the matrix is 3, but I struggle to understand the difference between when the rank is 1 and when the rank is 2. I understand that a matrix' rank is the number of non-zero rows in its row echelon matrix, but I struggle to understand what it tells me.
Let's say I have rank 2. Does it mean that I get a linear combination of 2 lines that provides the 3rd? If so, what does rank 1 get you?
I really hope the question is coherent. Thank you and have a blessed day.