Rank of a Matrix: Let M be a non-zero matrix. If r is the number of non-zero rows when it is
reduced to the reduced echelon form, then r is called the (row) rank of the matrix M.
Example:
Find rank the rank of matrix \begin{bmatrix} 1 &-1 &2 &-3 \\ 2 &0 &7 &-7 \\ 3 &1 &12 &-11 \end{bmatrix}
Solution:
\begin{bmatrix} 1 &-1 &2 &-3 \\ 2 &0 &7 &-7 \\ 3 &1 &12 &-11 \end{bmatrix} R\begin{bmatrix} 1 &-1 &2 &-3 \\ 0 &2 &3 &-1 \\ 0 &4 &6 &-2 \end{bmatrix}