Question

An ordered pair (α, β) for which the system of linear equations
(1 + α)x + βy + z = 2
αx + (1 + β)y + z = 3
αx + βy + 2z = 2
has a unique solution, is:
(A) (2, 4) (B) (–3, 1)
(C) (–4, 2) (D) (1, –3)

Answer 1

Answer:

options 1,2,4

Step-by-step explanation:

see attachment

for unique solutions

determinant not equal to zero

matrix formes by coffecient of x, y, z

should be singular

also see eq1

on solving I get

alpha -beta not equal to 2

also

we have to calculate

x= ∆1/∆, y=∆2/∆ ,z= ∆3/∆ ......1

so final conditions for unique solutions

delta, delta1, 2,3 all not equal to zero

we get beta not equal to 2 alpha not equal to -4

and from 3 deter.. beta not equal to 2

now see attachment s