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Question A.1: Find the rank of the matrix A = |1 4 5 2 6 8 3 7 22|...

Find the rank of the matrix

\overline{A}=\left|\begin{matrix} 1 & 4 & 5 \\ 2 & 6 & 8 \\ 3 & 7 & 22 \end{matrix} \right|
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This matrix can be reduced to an upper triangular matrix by elementary row operations (see the following):

\overline{A}=\left|\begin{matrix} 1 & 4 & 5 \\ 0 & 1 & 1 \\ 0 & 0 & 12 \end{matrix} \right|

The rank of the matrix is 3.

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