JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A , B , C\) be \(3 \times 3\) matrices such that \(A\) is symmetric and \(B\) and \(C\) are skew-symmetric.Consider the statements \((S1): A ^{13} B ^{26}- B ^{26} A ^{13}\) is symmetric \((S2):A ^{26} C ^{13}- C ^{13} A ^{26}\) is symmetric Then,
- A Only \(S 2\) is true
- B Only \(S 1\) is true
- C Both \(S 1\) and \(S 2\) are false
- D Both \(S1\) and \(S2\) are true
Answer & Solution
Correct Answer
(A) Only \(S 2\) is true
Step-by-step Solution
Detailed explanation
Given, \(A^T=A, B^T=-B, C^T=-C\) Let \(M=A^{13} B^{26}-B^{26} A^{13}\) Then, \(M^T=\left(A^{13} B^{26}-B^{26} A^{13}\right)^{ T }\) \(=\left(A^{13} B^{26}\right)^T-\left(B^{26} A^{13}\right)^{ T }\)…
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