$ \newcommand{\braket}[1]{\langle #1 \rangle} \newcommand{\abs}[2][]{\left\lvert#2\right\rvert_{\text{#1}}} \newcommand{\ket}[1]{\left\lvert#1 \right.\rangle} \newcommand{\bra}[1]{\langle\left. #1\right\rvert} \newcommand{\braket}[1]{\langle #1 \rangle} \newcommand{\dd}{\text{d}} \newcommand{\dv}[2]{\frac{\dd #1}{\dd #2}} \newcommand{\pdv}[2]{\frac{\partial}{\partial #1}} $
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A system of equations $$\begin{align*} a_{11}x_{1}+\dots + a_{1n}x_n&=y_1 \\ a_{21}x_1+\dots + a_{2n}x_n&=y_2 \\ \vdots \\ a_{m1}x_{1}+\dots + a_{mn}x_{n}&=y_{m} \end{align*}$$ is homogeneous if $y_1=y_2=\dots = y_m=0$.

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A system of equations $$\begin{align*} a_{11}x_{1}+\dots + a_{1n}x_n&=y_1 \\ a_{21}x_1+\dots + a_{2n}x_n&=y_2 \\ \vdots \\ a_{m1}x_{1}+\dots + a_{mn}x_{n}&=y_{m} \end{align*}$$ is homogeneous if $y_1=y_2=\dots = y_m=0$.

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definition
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A system of equations $$\begin{align*} a_{11}x_{1}+\dots + a_{1n}x_n&=y_1 \\ a_{21}x_1+\dots + a_{2n}x_n&=y_2 \\ \vdots \\ a_{m1}x_{1}+\dots + a_{mn}x_{n}&=y_{m} \end{align*}$$ is homogeneous if $y_1=y_2=\dots = y_m=0$.

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A system of equations $$\begin{align*} a_{11}x_{1}+\dots + a_{1n}x_n&=y_1 \\ a_{21}x_1+\dots + a_{2n}x_n&=y_2 \\ \vdots \\ a_{m1}x_{1}+\dots + a_{mn}x_{n}&=y_{m} \end{align*}$$ is homogeneous if $y_1=y_2=\dots = y_m=0$.

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definition
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