JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If the system of equations:
\(x+y+z=5\)
\(x+2y+3z=9\)
\(x+3y+\lambda z=\mu\)
has infinitely many solutions, then the value of \(\lambda+\mu\) is:
- A \(16\)
- B \(18\)
- C \(19\)
- D \(21\)
Answer & Solution
Correct Answer
(B) \(18\)
Step-by-step Solution
Detailed explanation
For the system to have infinitely many solutions, \(\Delta = 0\) and \(\Delta_x = \Delta_y = \Delta_z = 0\). \(\Delta = \begin{vmatrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 3 & \lambda \end{vmatrix} = 1(2\lambda - 9) - 1(\lambda - 3) + 1(3 - 2)\)…
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