Question

Construct a $3\times 4$ matrix whose elements $a_{ij}$ are given by $a_{ij}=i+2j$

Answer 1

The elements of a $3\times 4$ matrix are $A=\left[\begin{array}{cccc}{a}_{11}& a_{12}& a_{13}& a_{14}\\ a_{21}& a_{22}& a_{23}& a_{24}\\ a_{31}& a_{32}& a_{33}& a_{34}\end{array}\right]$

Applying the given rule: $a_{ij}=i+2j{a}_{11}=3,a_{12}=5,a_{13}=7,a_{14}=9a_{21}=4,a_{22}=6,a_{23}=8,a_{24}=10a_{31}=5,a_{32}=7,a_{33}=9,a_{34}=11$

Therefore $A=\left[\begin{array}{cccc}3& 5& 7& 9\\ 4& 6& 8& 10\\ 5& 7& 9& 11\end{array}\right]$ is the required matrix.