Class 12 Matrices · Short Answer2 Markssymmetric_and_skew_symmetric
Class 12 Maths · Matrices · Short Answer #53
Prove that every diagonal entry of a real skew-symmetric matrix is zero.
✅ Step-by-Step Solution
Final Answer: Every aᵢᵢ=0.
- A real skew-symmetric matrix satisfies Aᵀ=−A.
- For each diagonal position i, transposition leaves that entry fixed, so aᵢᵢ=−aᵢᵢ. Thus 2aᵢᵢ=0.
- Since the entries are real, aᵢᵢ=0 for every i.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] A real skew-symmetric matrix satisfies Aᵀ=−A.
- [1 mark] For each diagonal position i, transposition leaves that entry fixed, so aᵢᵢ=−aᵢᵢ. Thus 2aᵢᵢ=0.
- [0.5 marks] Since the entries are real, aᵢᵢ=0 for every i.
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