NCERT Class 12 · Ch 3 Exercise 3.3 · Q9
NCERT Class 12 Maths · Chapter 3 Matrices · Exercise 3.3 Question 9
Find (A+Aᵀ)/2 and (A−Aᵀ)/2 for A=\(\left[\begin{matrix}0 & a & b\\- a & 0 & c\\- b & - c & 0\end{matrix}\right]\).
💡 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: Symmetric part O₃; skew-symmetric part A.
- Direct transposition gives Aᵀ=\(\left[\begin{matrix}0 & - a & - b\\a & 0 & - c\\b & c & 0\end{matrix}\right]\)=−A.
- Thus (A+Aᵀ)/2=(A−A)/2=O, and (A−Aᵀ)/2=(A+A)/2=A.
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