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-

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 \dots (4)

4 x_{1} + x_{2} + (a^{2} - 14) x_{3} = a + 2 \dots (3)

(4) - (3) :

(4 + a) (4 - a) x_{3} = 4 - a \dots (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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