Question

Construct a $3\times 2$ matrix whose elements are given by $a_1=\frac{1}{2}|i-3j|$.

Answer 1

$a_{11}=\frac{1}{2}|-2|=1$; $a_{12}=\frac{1}{2}|1-6|=\frac{5}{2}$

$a_{21}=\frac{1}{2}|2-3|=\frac{1}{2}$; $a_{22}=\frac{1}{2}|2-6|=2$

$a_{31}=\frac{1}{2}|3-3|=0$; $a_{32}=\frac{1}{2}|3-6|=\frac{3}{2}$

$\Rightarrow M=\left[\begin{array}{cc}1& 5/2\\ 1/2& 2\\ 0& 3/2\end{array}\right]$.