AP EAMCET · Maths · Determinants
The system of equations \(x+y+z=5, x+2 y+3 z=9\) and \(x+3 y+\lambda z=\mu\) has unique solution if
- A \(\lambda=5, \mu=10\)
- B \(\lambda=5, \mu \neq 10\)
- C \(\lambda \in \mathbb{R}, \mu \neq 5\)
- D \(\lambda \neq 5, \mu \in \mathbb{R}\)
Answer & Solution
Correct Answer
(D) \(\lambda \neq 5, \mu \in \mathbb{R}\)
Step-by-step Solution
Detailed explanation
Matrix determinant: \( \begin{vmatrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 3 & \lambda \end{vmatrix} \) \( D = 1(2\lambda - 9) - 1(\lambda - 3) + 1(3 - 2) \) \( D = 2\lambda - 9 - \lambda + 3 + 1 \) \( D = \lambda - 5 \) For unique solution, \( D \neq 0 \) \( \lambda - 5 \neq 0 \)…
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