For questions regarding the rank of matrices in linear algebra.

In linear algebra, the rank of a matrix $A$ is the size of the largest collection of linearly independent columns of $A$ (the column rank) or the size of the largest collection of linearly independent rows of $A$ (the row rank). For every matrix, the column rank is equal to the row rank. It is a measure of the “nondegenerateness” of the system of linear equations and linear transformation encoded by $A$. There are multiple definitions of rank. The rank is one of the fundamental pieces of data associated with a matrix.

If $A$ is the matrix of a linear map $f$, then the rank of $A$ is equal to the dimension of the image of $f$.