JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If the system of equations \(2 x+y-z=5\) \(2 x-5 y+\lambda z=\mu\) \(x+2 y-5 z=7\) has infinitely many solutions, then \((\lambda+\mu)^2+(\lambda-\mu)^2\) is equal to
- A \(916\)
- B \(912\)
- C \(920\)
- D \(904\)
Answer & Solution
Correct Answer
(A) \(916\)
Step-by-step Solution
Detailed explanation
\(\left|\begin{array}{ccc}2 & 1 & -1 \\ 2 & -5 & \lambda \\ 1 & 2 & -5\end{array}\right|=0\) \(2(25-2 \lambda)-(-10-\lambda)-(4+5)=0\) \(50-4 \lambda+10+\lambda-9=0\) \(51=3 \lambda \Rightarrow \lambda=17\)…
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