NCERT Class 12 · Ch 3 Exercise 3.3 · Q8
NCERT Class 12 Maths · Chapter 3 Matrices · Exercise 3.3 Question 8
For A=\(\left[\begin{matrix}1 & 5\\6 & 7\end{matrix}\right]\), verify (i) A+Aᵀ is symmetric; (ii) A−Aᵀ is skew symmetric.
💡 Concept Hints
- Check the matrix orders and the meaning of the requested operation before calculating.
- Keep row and column indices in order. Compare corresponding entries only after the matrix expressions have compatible dimensions.
✅ Step-by-Step Solution
Final Answer: A+Aᵀ=\(\left[\begin{matrix}2 & 11\\11 & 14\end{matrix}\right]\); A−Aᵀ=\(\left[\begin{matrix}0 & -1\\1 & 0\end{matrix}\right]\).
- Aᵀ=\(\left[\begin{matrix}1 & 6\\5 & 7\end{matrix}\right]\).
- The sum is \(\left[\begin{matrix}2 & 11\\11 & 14\end{matrix}\right]\); its transpose equals itself.
- The difference is \(\left[\begin{matrix}0 & -1\\1 & 0\end{matrix}\right]\); its transpose equals its negative.
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