Construct a 2 × 2 matrix, where $a_{ij}=\frac{(i-2j)^2}{2}$
Answer & explanation
Correct answer: option 1
We have, $A = [a_{ij}]_{2 × 2}$
Such that, $a_{ij}=\frac{(i-2j)^2}{2}$; where $1≤i≤2; 1≤j≤2$
$∴a_{11}=\frac{(1-2)^2}{2}=\frac{1}{2}$
$a_{12}=\frac{(1-2× 2)^2}{2}=\frac{9}{2}$
$a_{21}=\frac{(2-2× 1)^2}{2}=0$
$a_{22}=\frac{(2-2× 2)^2}{2}=2$
So, $A=\begin{bmatrix}\frac{1}{2}&\frac{9}{2}\\0&2\end{bmatrix}$