Solve the following equation x + 2y + 2z = 0 2x + y − 2z =0 3x + 4y − 6z =0 3x − 11y + 12z = 0


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Question Number 197470 by Mastermind last updated on 18/Sep/23

$S o l v e t h e f o l l o w i n g e q u a t i o n$ $x + 2 y + 2 z = 0$ $2 x + y - 2 z = 0$ $3 x + 4 y - 6 z = 0$ $3 x - 11 y + 12 z = 0$
	Answered by MathedUp last updated on 19/Sep/23

	$A B = O A = (\begin{matrix} 1 & 2 & 2 \\ 2 & 1 & - 2 \\ 3 & 4 & - 6 \end{matrix}), B = (\begin{matrix} x \\ y \\ z \end{matrix}), O = (\begin{matrix} 0 \\ 0 \\ 0 \end{matrix})$ $B = A^{- 1} O$ $B = O$ $x, y, z = 0$
	Commented by Mastermind last updated on 25/Sep/23

	$A n o t h e r i l l u s t r a t i o n, T h a n k y o u M A N$
	Answered by deleteduser1 last updated on 18/Sep/23

	$(i) + (i i) \Rightarrow 3 (x + y) = 0 \Rightarrow x = - y$ $(i) \Rightarrow y = - 2 z$ $(x, - x, \frac{x}{2}) \Rightarrow (x, y, z) = (0, 0, 0)$
	Commented by Mastermind last updated on 18/Sep/23

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