(i) Given \[{{a}_{i\text{ }j}}~=\text{ }2i\text{ }+\text{ }i/j\]
Let \[A\text{ }=\text{ }{{[{{a}_{i\text{ }j}}]}_{4\times 3}}\]
So, the elements in a \[4\text{ }\times \text{ }3\] matrix are
\[{{a}_{11}},\text{ }{{a}_{12}},\text{ }{{a}_{13}},\text{ }{{a}_{21}},\text{ }{{a}_{22}},\text{ }{{a}_{23}},\text{ }{{a}_{31,~}}{{a}_{32,~}}{{a}_{33,~}}{{a}_{41,}}~{{a}_{42,}}~{{a}_{43}}\]
\[A\text{ }=\]
\[{{a}_{11}}~=\]
\[{{a}_{12}}~=\]
\[{{a}_{13}}~=\]
\[{{a}_{21}}~=\]
\[{{a}_{22}}~=\]
\[{{a}_{23}}~=\]
\[{{a}_{31}}~=\]
\[{{a}_{32}}~=\]
\[{{a}_{33}}~=\]
\[{{a}_{41}}~=\]
\[{{a}_{42}}~=\]
\[{{a}_{43}}~=\]
Substituting these values in matrix A we get,
\[A\text{ }=\]
(ii) Given \[{{a}_{i\text{ }j}}~=\text{ }\left( i\text{ }-\text{ }j \right)/\text{ }\left( i\text{ }+\text{ }j \right)\]
Let \[A\text{ }=\text{ }{{[{{a}_{i\text{ }j}}]}_{4\times 3}}\]
So, the elements in a \[4\text{ }\times \text{ }3\] matrix are
\[{{a}_{11}},\text{ }{{a}_{12}},\text{ }{{a}_{13}},\text{ }{{a}_{21}},\text{ }{{a}_{22}},\text{ }{{a}_{23}},\text{ }{{a}_{31,~}}{{a}_{32,~}}{{a}_{33,~}}{{a}_{41,}}~{{a}_{42,}}~{{a}_{43}}\]
\[A\text{ }=\]
\[{{a}_{11}}~=\]
\[{{a}_{12}}~=\]
\[{{a}_{13}}~=\]
\[{{a}_{21}}~=\]
\[{{a}_{22}}~=\]
\[{{a}_{23}}~=\]
\[{{a}_{31}}~=\]
\[{{a}_{32}}~=\]
\[{{a}_{33}}~=\]
\[{{a}_{41}}~=\]
\[{{a}_{42}}~=\]
\[{{a}_{43}}~=\]
Substituting these values in matrix A we get,
\[A\text{ }=\]
