> [!summary]
A dependent variable is a variable in a reduced system of linear system with a leading 1.
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# Definition
A dependent variable is a variable in a system of [[Linear Equations|linear equations]] that is solved in terms of other variables (such as [[Free Variables|free variables]]). When a system of linear equations is reduced, a dependent variable will have a [[Leading 1s|pivot]].
# Examples
> [!example] Finding the dependent variable in a reduced linear system
>
Given the augmented matrix in [[Reduced Row Echelon Form|reduced row echelon form]]:
> $
\left[
\begin{array}{ccc|c}
\color{blue}{1} & 0 & {2} & 3 \\
0 & \color{blue}{1} & {-1} & 4 \\
0 & 0 & {0} & 0 \\
\end{array}
\right]
> $
The blue entries are a dependent variable they have their own leading ones in a reduced system
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