# Definition of homogeneous linear system of equations

Put content here.**Definition:** A **homogeneous linear system** is a system of the form $Ax = 0$, where every constant term on the right-hand side is zero.
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Written out:
$$\begin{cases}\n a_{11} x_1 + a_{12} x_2 + \cdots + a_{1n} x_n = 0 \\\n a_{21} x_1 + a_{22} x_2 + \cdots + a_{2n} x_n = 0 \\\n \quad\vdots \\\n a_{m1} x_1 + a_{m2} x_2 + \cdots + a_{mn} x_n = 0\n\end{cases}$$
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Every homogeneous system is consistent because $x = 0$ is always a solution (the **trivial solution**).
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**Example:**
$$\begin{cases} x + y - z = 0 \\ 2x - y + 3z = 0 \end{cases}$$

# Parents

* Linear systems of equations