Rank of a matrix:

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}

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