Тhe rank of a matrix
A common approach to finding the rank of a matrix is to reduce it to a simpler form, generally row echelon form, by elementary row operations.
A fundamental result in linear algebra is that the column rank and the row rank are always equal.
A matrix is said to have full rank if its rank equals the largest possible for a matrix of the same dimensions, which is the lesser of the number of rows and columns.
A matrix is said to be rank-deficient if it does not have full rank. The rank deficiency of a matrix is the difference between the lesser of the number of rows and columns, and the rank.