Question:
If the matrix \(A = \left[ \begin{array}{cc}1 & -1 4\lambda & 8 \end{array} \right]\) is singular, then the value of \(\lambda\) is equal to
If the matrix \(A = \left[ \begin{array}{cc}1 & -1 4\lambda & 8 \end{array} \right]\) is singular, then the value of \(\lambda\) is equal to
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For \(2\times2\) matrix, singular if \(ad = bc\).
Updated On: Apr 25, 2026
- -2
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept:
Singular means determinant = 0. \(\det A = 1\cdot8 - (-1)(4\lambda) = 8 + 4\lambda = 0 \implies \lambda = -2\).
Step 2: Detailed Explanation:
\(\det = ad - bc = 8 - (-4\lambda) = 8+4\lambda = 0\). So \(\lambda = -2\).
Step 3: Final Answer:
Option (A).
Singular means determinant = 0. \(\det A = 1\cdot8 - (-1)(4\lambda) = 8 + 4\lambda = 0 \implies \lambda = -2\).
Step 2: Detailed Explanation:
\(\det = ad - bc = 8 - (-4\lambda) = 8+4\lambda = 0\). So \(\lambda = -2\).
Step 3: Final Answer:
Option (A).
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