JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
The system of linear equations \(x + \lambda y - z = 0,\lambda x - y - z = 0\;,\;x + y - \lambda z = 0\) has a non-trivial solution for:
- A exactly two values of \(\lambda \)
- B exactly three values of \(\;\lambda \)
- C infinitely many values of \(\lambda \)
- D exactly one value of \(\;\lambda \)
Answer & Solution
Correct Answer
(B) exactly three values of \(\;\lambda \)
Step-by-step Solution
Detailed explanation
Cramer's rule for solving system of linear equations - When \(\Delta=0\) and \(\Delta_{1}=\Delta_{2}=\Delta_{3}=0\) then the system of equations has infinite solutions. -wherein \(a_{1} x+b_{1} y+c_{1} z=d_{1}\) \(a_{2} x+b_{2} y+c_{2} z=d_{2}\) \(a_{3} x+b_{3} y+c_{3} z=d_{3}\)…
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