NCERT Class 12 Maths · Chapter 3 Matrices · Exercise 3.1 Question 4

✅ Step-by-Step Solution

1. Use indices i=1,…,2 and j=1,…,2. Fill one row at a time.
2. Part 1: aᵢⱼ=(i+j)²/2. For each fixed i, substitute every j in order; the resulting matrix is \(\left[\begin{matrix}2 & \frac{9}{2}\\\frac{9}{2} & 8\end{matrix}\right]\).
3. Part 2: aᵢⱼ=i/j. For each fixed i, substitute every j in order; the resulting matrix is \(\left[\begin{matrix}1 & \frac{1}{2}\\2 & 1\end{matrix}\right]\).
4. Part 3: aᵢⱼ=(i+2j)²/2. For each fixed i, substitute every j in order; the resulting matrix is \(\left[\begin{matrix}\frac{9}{2} & \frac{25}{2}\\8 & 18\end{matrix}\right]\).