JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let the system of linear equations \(x +2 y + z =2\), \(\alpha x +3 y - z =\alpha,-\alpha x + y +2 z =-\alpha\) be inconsistent. Then \(\alpha\) is equal to
- A \(\frac{5}{2}\)
- B \(\frac{7}{2}\)
- C \(-\frac{7}{2}\)
- D \(-\frac{5}{2}\)
Answer & Solution
Correct Answer
(C) \(-\frac{7}{2}\)
Step-by-step Solution
Detailed explanation
\(\Delta=\left|\begin{array}{ccc} 1 & 2 & 1 \\ 2 & 3 & -1 \\ -2 & 1 & 2 \end{array}\right|\) \(=(6+ y )-2((2 \alpha-\alpha)+1(\alpha+3 \alpha)\) \(=7-2 \alpha+4 \alpha\) \(=7+2 \alpha\) \(\Delta=0 \Rightarrow \alpha=-\frac{7}{2}\)…
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