Show-that-for-the-system-of-equations-x-y-z-3-2x-2y-2z-6-3x-3y-3z-9-the-general-solution-is-given-by-x-1-

Question Number 908 by 112358 last updated on 20/Apr/15

S h o w t h a t f o r t h e s y s t e m o f

e q u a t i o n s

x + y + z = 3

2 x + 2 y + 2 z = 6

3 x + 3 y + 3 z = 9

t h e g e n e r a l s o l u t i o n i s g i v e n b y

x = λ + 1

y = μ + 1

z = - λ - μ + 1

w h e r e λ, μ \in R .

Commented by prakash jain last updated on 21/Apr/15

Only one equation is given

x + y + z = 3

Two variable can be independently chosen .

Any value can be chosen for x a n d y .

If x = λ + 1, y = μ + 1

x + y + z = 3

z = 3 - x - y = 1 - λ - μ

λ, μ can be real or complex .

For the general solution λ, μ need not be real .