Given the system of linear equation x_1 +2x_2 −3x_3 =4 3x_1 −x_2 +5x_3 =2 4x_1 +x_2 +(a^2 −14)x_3 =a+2 for which value of “a” the system have one solution,infinite sol.and number solution.


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Question Number 124071 by zarminaawan last updated on 30/Nov/20

$G i v e n t h e s y s t e m o f l i n e a r e q u a t i o n$ $x_{1} + 2 x_{2} - 3 x_{3} = 4$ $3 x_{1} - x_{2} + 5 x_{3} = 2$ $4 x_{1} + x_{2} + (a^{2} - 14) x_{3} = a + 2$ $f o r w h i c h v a l u e o f ‘ ‘ a^{″} t h e s y s t e m h a v e o n e s o l u t i o n, i n f i n i t e s o l . a n d n u m b e r s o l u t i o n .$
Commented by danishnaveed last updated on 30/Nov/20

$s e n d a n s$
	Answered by mr W last updated on 30/Nov/20

	$(1) + (2) :$ $4 x_{1} + x_{2} + 2 x_{3} = 6 . . . (4)$ $4 x_{1} + x_{2} + (a^{2} - 14) x_{3} = a + 2 . . . (3)$ $(4) - (3) :$ $(4 + a) (4 - a) x_{3} = 4 - a . . . (5)$ $i f a = 4 \Rightarrow i n f i n i t e s o l u t i o n s$ $i f a = - 4 \Rightarrow n o s o l u t i o n$ $i f a \neq 4 & a \neq - 4 \Rightarrow o n e s o l u t i o n x_{3} = \frac{1}{a + 4}$
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