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# 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}

## Author: Azhar Ali

I am graduated in Mathematics from university of Sargodha, having master degree in Mathematics. Mathematics blogger