Problem:
Compute the rank of
$\left(
\begin{array}{ccc}
 -2 & -4 & 3 \\
\end{array}
\right)$.
Answer:
\begin{array}{l}
 
\begin{array}{l}
 \text{Find the rank of the matrix}: \\
 M=\left(
\begin{array}{ccc}
 -2 & -4 & 3 \\
\end{array}
\right) \\
\end{array}
 \\
\hline
 
\begin{array}{l}
 \text{As }\text{each }\text{row }\text{of }\text{matrix }M \text{has }\text{only }\text{zeroes }\text{to }\text{the }\text{left }\text{of }\text{the }\text{main }\text{diagonal, }\text{it }\text{is }\text{in }\text{row }\text{echelon }\text{form}: \\
 \left(
\begin{array}{ccc}
 -2 & -4 & 3 \\
\end{array}
\right) \\
\end{array}
 \\
 
\begin{array}{l}
 \text{There }\text{is }1 \text{nonzero }\text{row }\text{in }\text{the }\text{row }\text{echelon }\text{matrix, }\text{so }\text{the }\text{rank }\text{is }1: \\
 \fbox{$
\begin{array}{ll}
 \text{Answer:} &  \\
 \text{} & \text{rank}\left(
\begin{array}{ccc}
 -2 & -4 & 3 \\
\end{array}
\right)=1 \\
\end{array}
$} \\
\end{array}
 \\
\end{array}

{'source': 'AMPS', 'file': 'amps/mathematica/linear_algebra/rank_and_nullity_w_steps/1551.txt'}