Solve completely the equations
$x + 3 y - 2 z = 0, 2 x - y + 4 z = 0, x - 11 y + 14 z = 0$ .

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Solution

$x + 3 y - 2 z = 0$
$2 x - y + 4 z = 0$
$x - 11 y + 14 z = 0$
$A x = B \Rightarrow x = \to A B$
$⎡ ⎢ ⎣ \begin{matrix} 1 & 3 & - 2 2 & - 1 & 4 1 & - 11 & 14 \end{matrix} ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ \begin{matrix} x y z \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 000 \end{matrix} ⎤ ⎥ ⎦$
$⎡ ⎢ ⎣ \begin{matrix} x y z \end{matrix} ⎤ ⎥ ⎦ = {⎡ ⎢ ⎣ \begin{matrix} 1 & 3 & - 2 2 & - 1 & 4 1 & - 11 & 14 \end{matrix} ⎤ ⎥ ⎦}^{- 2} ⎡ ⎢ ⎣ \begin{matrix} 000 \end{matrix} ⎤ ⎥ ⎦$
$⎡ ⎢ ⎣ \begin{matrix} x y z \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 000 \end{matrix} ⎤ ⎥ ⎦$
$x = y = z = 0$

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x + 3 y - 2 z = 0 2 x - y + 4 z = 0 x - 11 y + 14 z = 0

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