# I need to calculate the rank of the matrix A,

I need to calculate the rank of the matrix A, shown below:
$\left[\begin{array}{ccc}3& 2& -1\\ 2& -3& -5\\ -1& -4& -3\end{array}\right]$
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George Spencer

Simply use row reduction: the rank is the number of non-zero rows after you've performed row reduction:
$\left[\begin{array}{ccc}3& 2& -1\\ 2& -3& -5\\ -1& -4& -3\end{array}\right]⇝\left[\begin{array}{ccc}1& 4& 3\\ 3& 2& -1\\ 2& -3& -5\end{array}\right]⇝\left[\begin{array}{ccc}1& 4& 3\\ 0& -10& -10\\ 0& -11& -11\end{array}\right]\to \left[\begin{array}{ccc}1& 4& 3\\ 0& 1& 1\\ 0& -11& -11\end{array}\right]⇝\left[\begin{array}{ccc}1& 4& 3\\ 0& 1& 1\\ 0& 0& 0\end{array}\right]$

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Ourst1977
I am looking for a solution myself, I will be grateful for help with the solution