Question

Construct a $2\times 2$ matrix $A=\left[a_{ij}\right]$ whose elements are given by $\frac{1}{2}|-3i+j|$.

Answer 1

$A_{ij}=\frac{1}{2}|-3i+j|$

$A_{11}=\frac{1}{2}|-3+1|=1$

$A_{12}=\frac{1}{2}|-3+2|=\frac{-1}{2}$

$A_{21}=\frac{1}{2}|-6+1|=\frac{5}{2}$

$A_{22}=\frac{1}{2}|-6+2|=2$

$A=\left[\begin{array}{cc}1& \frac{-1}{2}\\ \frac{5}{2}& 2\end{array}\right]$