The system has unique solution, if

Question

Consider the system of equations

x + 2y – z = 2 .....(i)

x – y + 2z = 3 .....(ii)

2x + y – z = 5 .....(iii)

3x + 2y + pz = q.....(iv)

The system has unique solution, if

(A) p = 0, q = 22/3

(B) p = 1, q = 20/3

(C) p = 1, q = 22/3

(D) p = q = 22/3

Answer 1

Correct Option :- (A) (C) (D)

Explanation :-

x + 2y – z = 2 ......... (1)

x – y + 2z = 3 ........ (2)

2x + y – z = 5 ......... (3)

3x+2y+pz = q ........... (4)

First three equation gives

x = 8/3 , y = -1/3 , z = 0

for unique solutions p ∈ R, q = 22/3