NCERT Class 12 Maths · Chapter 3 Matrices · Exercise 3.3 Question 1

✅ Step-by-Step Solution

1. A transpose turns row i into column i: (Aᵀ)ᵢⱼ=Aⱼᵢ.
2. Part (1): the original order is 4×1; the transpose has order 1×4 and equals \(\left[\begin{matrix}5 & 1 & 2 & -1\end{matrix}\right]\).
3. Part (2): the original order is 2×2; the transpose has order 2×2 and equals \(\left[\begin{matrix}1 & 2\\-1 & 3\end{matrix}\right]\).
4. Part (3): the original order is 3×3; the transpose has order 3×3 and equals \(\left[\begin{matrix}-1 & 3 & 2\\5 & 5 & 3\\6 & 6 & -1\end{matrix}\right]\).