NCERT Class 12 Maths · Chapter 3 Matrices · Exercise 3.3 Question 3

✅ Step-by-Step Solution

1. First A = \(\left[\begin{matrix}3 & -1 & 0\\4 & 2 & 1\end{matrix}\right]\), B = \(\left[\begin{matrix}-1 & 2 & 1\\1 & 2 & 3\end{matrix}\right]\).
2. Aᵀ = \(\left[\begin{matrix}3 & 4\\-1 & 2\\0 & 1\end{matrix}\right]\), Bᵀ = \(\left[\begin{matrix}-1 & 1\\2 & 2\\1 & 3\end{matrix}\right]\).
3. (i) A+B=\(\left[\begin{matrix}2 & 1 & 1\\5 & 4 & 4\end{matrix}\right]\), so (A+B)ᵀ=\(\left[\begin{matrix}2 & 5\\1 & 4\\1 & 4\end{matrix}\right]\)=Aᵀ+Bᵀ.
4. (ii) A−B=\(\left[\begin{matrix}4 & -3 & -1\\3 & 0 & -2\end{matrix}\right]\), so (A−B)ᵀ=\(\left[\begin{matrix}4 & 3\\-3 & 0\\-1 & -2\end{matrix}\right]\)=Aᵀ−Bᵀ.