Question

Construct a 2 × 2 matrix A = [a_ij] whose elements a_ij are given by \[a_{ij} = \begin{cases}\frac{\left| - 3i + j \right|}{2} & , if i \neq j \\ \left( i + j \right)^2 & , if i = j\end{cases}\]

 

Answer 1

\[a_{ij} = \begin{cases}\frac{\left| - 3i + j \right|}{2} & , if i \neq j \\ \left( i + j \right)^2 & , if i = j\end{cases}\]

\[a_{11} = \left( 1 + 1 \right)^2 = 4\] 

\[ a_{12} = \frac{\left| - 3 \times 1 + 2 \right|}{2} = \frac{1}{2}\] 

\[ a_{21} = \frac{\left| - 3 \times 2 + 1 \right|}{2} = \frac{5}{2}\] 

\[ a_{22} = \left( 2 + 2 \right)^2 = 16\] 

\[\text{Hence, the matrix A} = \begin{bmatrix}4 & \frac{1}{2} \\ \frac{5}{2} & 16\end{bmatrix} .\]