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}<br>1 &-1 &2 &-3 \\<br>2 &0 &7 &-7 \\<br>3 &1 &12 &-11<br>\end{bmatrix}
Solution:
\begin{bmatrix}<br>1 &-1 &2 &-3 \\<br>2 &0 &7 &-7 \\<br>3 &1 &12 &-11<br>\end{bmatrix} R\begin{bmatrix}<br>1 &-1 &2 &-3 \\<br>0 &2 &3 &-1 \\<br>0 &4 &6 &-2<br>\end{bmatrix}