CUET · MATHS · PYQ PAPER 2025
If the matrix \(\left[\begin{array}{ccc}2 & -1 & 3 \\ \lambda & 0 & 7 \\ -1 & 1 & 4\end{array}\right]\) is not invertible, then the value of \(\lambda\) is :
- A 0
- B \(-1\)
- C 1
- D \(\frac{1}{2}\)
Answer & Solution
Correct Answer
(C) 1
Step-by-step Solution
Detailed explanation
\(\det(A) = 0\) \(2(0 \cdot 4 - 7 \cdot 1) - (-1)(\lambda \cdot 4 - 7 \cdot (-1)) + 3(\lambda \cdot 1 - 0 \cdot (-1)) = 0\) \(2(-7) + (4\lambda + 7) + 3\lambda = 0\) \(-14 + 4\lambda + 7 + 3\lambda = 0\) \(7\lambda - 7 = 0\) \(7\lambda = 7\) \(\lambda = 1\)
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