JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(\lambda \) be a real number for which the system of linear equations \(x + y + z = 6\)
; \(4x + \lambda y - \lambda z = \lambda - 2\) ; \(3x + 2y -4z = -5\) Has indefinitely many solutions. Then \(\lambda \) is a root of the quadratic equation
- A \({\lambda ^2} - \lambda - 6\, = 0\)
- B \({\lambda ^2} - 3\lambda - 4 = 0\)
- C \({\lambda ^2} + 3\lambda - 4 = 0\)
- D \({\lambda ^2} + \lambda - 6 = 0\)
Answer & Solution
Correct Answer
(A) \({\lambda ^2} - \lambda - 6\, = 0\)
Step-by-step Solution
Detailed explanation
\(D=0\) \(\left| {\begin{array}{*{20}{c}} 1&1&1\\ 4&\lambda &\lambda \\ 3&2&{ - 4} \end{array}} \right| = 0 \Rightarrow \lambda = 3\)
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