Question

The Rank of the following matrix is

$\left[\begin{array}{cccc}1& 0& 0& 3\\ 0& 1& 1& 2\\ 0& 0& 0& 0\\ 0& 0& 1& 1\end{array}\right]-----------$

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Answer 1

Lets convert it into Echelon form

For that all no zero rows should be below all zero rows.

Interchange, $R_3$ & $R_4$

$\left[\begin{array}{cccc}1& 0& 0& 3\\ 0& 1& 1& 2\\ 0& 0& 1& 1\\ 0& 0& 0& 0\end{array}\right]$

This is now in Echelon form and the number of non zero rows are 3. Therefore Rank is 3.