CUET · MATHS · PYQ PAPER 2023
If \(A=\left[\begin{array}{ccc}0 & 2 & c \\ a & b & -1 \\ -5 & 1 & 0\end{array}\right]\) is a skew-symmetric matrix, then \((a+b+c)^3=\)
- A \(-125\)
- B \(0\)
- C 27
- D 343
Answer & Solution
Correct Answer
(C) 27
Step-by-step Solution
Detailed explanation
\(A^T = -A\) \(a_{ii} = 0 \Rightarrow b = 0\) \(a_{12} = -a_{21} \Rightarrow 2 = -a \Rightarrow a = -2\) \(a_{13} = -a_{31} \Rightarrow c = -(-5) \Rightarrow c = 5\) \(a+b+c = -2 + 0 + 5 = 3\) \((a+b+c)^3 = (3)^3 = 27\)
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