JEE Main202313 Apr 2023Morning ShiftMathematicsDeterminantsActual
For the system of linear equations 2 x + 4 y + 2 a z = b x + 2 y + 3 z = 4 2 x + 5 y + 2 z = 8 which of the following is NOT correct?
Options
- AIt has unique solution if a = b = 6
- BIt has infinitely many solutions if a = 3 ,   b = 6
- CIt has infinitely many solutions if a = 3 ,   b = 8
- DIt has unique solution if a = b = 8
Correct answer
B. It has infinitely many solutions if a = 3 ,   b = 6
Step-by-step solution
Given, System of linear equations, 2 x + 4 y + 2 a z = b x + 2 y + 3 z = 4 x + 2 y + 3 z = 4 Now finding, △ = 2 4 2 a 1 2 3 2 - 5 2 ⇒ △ = - 18 a - 3 Hence, for a = 3 ,   △ = 0 Now finding, △ 3 = b 2 4 4 1 2 8 2 - 5 ⇒ △ 3 = 9 b - 8 So, for b = 8 ,   △ 3 = 0 Now solving options we get, If a = 3 and b = 8 we'll have infinite solution For a = 8 , b = 8 ,   △ ≠ 0 ,   △ 3 = 0 ⇒ unique solution For a = b = 6 ,   △ &#