Solve : x_1 + 2x_2 − 3x_3 = 0 2x_1 + 4x_2 − 2x_3 = 2 3x_1 + 6x_2 − 4x


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Question Number 180446 by Mastermind last updated on 12/Nov/22

$Solve :$ $x_{1} + {2 x}_{2} - {3 x}_{3} = 0$ ${2 x}_{1} + {4 x}_{2} - {2 x}_{3} = 2$ ${3 x}_{1} + {6 x}_{2} - {4 x}_{3} = 3$
	Answered by liuxinnan last updated on 12/Nov/22


	Commented by liuxinnan last updated on 12/Nov/22

	Answered by mr W last updated on 12/Nov/22

	$f r o m e q n . (i) w e g e t :$ $2 x_{1} + 4 x_{2} = 6 x_{3} . . . (i v)$ $f r o m (i i) a n d (i v) :$ $6 x_{3} = 2 + 2 x_{3}$ $\Rightarrow x_{3} = \frac{1}{2}$ $f r o m e q n . (i) w e g e t :$ $3 x_{1} + 6 x_{2} = 9 x_{3} . . . (v)$ $f r o m (i i i) a n d (v) :$ $9 x_{3} = 3 + 4 x_{3}$ $\Rightarrow x_{3} = \frac{3}{5}$ $t h i s i s c o n t r a d i c t i o n t o x_{3} = \frac{1}{2} .$ $t h a t m e a n s t h e e q n . s y s t e m h a s n o$ $s o l u t i o n .$
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