JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
For the system of linear equations \(2 x-y+3 z=5\) \(3 x+2 y-z=7\) \(4 x+5 y+\alpha z=\beta\) Which of the following is NOT correct ?
- A The system has infinitely many solutions for \(\alpha=-5\) and \(\beta=9\)
- B The system has a unique solution for \(\alpha \neq-5\) and \(\beta=8\)
- C The system has infinitely many solutions for \(\alpha=-6\) and \(\beta=9\)
- D The system is inconsistent for \(\alpha=-5\) and \(\beta=8\)
Answer & Solution
Correct Answer
(C) The system has infinitely many solutions for \(\alpha=-6\) and \(\beta=9\)
Step-by-step Solution
Detailed explanation
\(\Delta=\left|\begin{array}{ccc}2 & -1 & 3 \\ 3 & 2 & -1 \\ 4 & 5 & \alpha\end{array}\right|=7(\alpha+5)\) \(\Delta_1=\left|\begin{array}{ccc}5 & -1 & 3 \\ 7 & 2 & -1 \\ \beta & 5 & \alpha\end{array}\right|=17 \alpha-5 \beta+130\)…
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