The system of linear equations
- A.has infinitely many solutions for
- B.is inconsistent when
- C.has a unique solution for
- D.is inconsistent when
Show answer and solution
Correct option: D
Solution
Subtract the second equation from the third: (a²-1-2)z = (a+1-5), giving (a²-3)z = a-4.
From equations 1 and 2: subtract eq1 from eq2 to get x + 2y + z = 3, then with eq1: y = 1, and x + z = 1.
The third equation reduces to (a²-3)z = a-4. When |a| = √3, a² = 3, so left side = 0 but right side = √3-4 ≠ 0 (for a = √3) or -√3-4 ≠ 0 (for a = -√3). In both cases 0 = a-4 is not satisfied, making the system inconsistent.
From equations 1 and 2: subtract eq1 from eq2 to get x + 2y + z = 3, then with eq1: y = 1, and x + z = 1.
The third equation reduces to (a²-3)z = a-4. When |a| = √3, a² = 3, so left side = 0 but right side = √3-4 ≠ 0 (for a = √3) or -√3-4 ≠ 0 (for a = -√3). In both cases 0 = a-4 is not satisfied, making the system inconsistent.
[JEE Main 2019 · 9 Jan · Shift I]