JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If the system of linear equations \(x + y + z = 5\) ; \(x = 2y + 2z = 6\) ; \(x + 3y + \lambda z = u (\lambda \, \mu \in R)\), has infinitely many solutions then the value of \(\lambda + \mu \) is
- A \(12\)
- B \(7\)
- C \(10\)
- D \(9\)
Answer & Solution
Correct Answer
(C) \(10\)
Step-by-step Solution
Detailed explanation
\(x + 3y + \lambda z - u = a\left( {x + y + z - 5} \right) + b\left( {x + 2y + 2z - 6} \right)\) Comparing coefficients we get \(a+b=1\) and \(a+2b=3\) \((a,b)=(-1,2)\) So, \(x + 3y + \lambda z - u = x + 3y + 3z - \lambda \) \( \Rightarrow u = 7,\lambda = 3\)
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