(i) Given
\[{{a}_{i\text{ }j~}}=\text{ }i\text{ }+\text{ }j\]
Let
\[A\text{ }=\text{ }[a{{~}_{i\text{ }j}}]{{~}_{2\times 3}}\]
So, the elements in a \[2\text{ }\times \text{ }3\] matrix are
\[{{a}_{11}},\text{ }{{a}_{12}},\text{ }{{a}_{13}},\text{ }{{a}_{21}},\text{ }{{a}_{22}},\text{ }{{a}_{23}}\]
\[{{a}_{11}}~=\text{ }1\text{ }+\text{ }1\text{ }=\text{ }2\]
\[{{a}_{12}}~=\text{ }1\text{ }+\text{ }2\text{ }=\text{ }3\]
\[{{a}_{13}}~=\text{ }1\text{ }+\text{ }3\text{ }=\text{ }4\]
\[{{a}_{21}}~=\text{ }2\text{ }+\text{ }1\text{ }=\text{ }3\]
\[{{a}_{22}}~=\text{ }2\text{ }+\text{ }2\text{ }=\text{ }4\]
\[{{a}_{23}}~=\text{ }2\text{ }+\text{ }3\text{ }=\text{ }5\]
Substituting these values in matrix A we get,
(ii) Given
\[{{a}_{i\text{ }j}}~=\text{ }{{\left( i\text{ }+\text{ }j \right)}^{2}}/2\]
Let
\[A\text{ }=\text{ }{{[{{a}_{i\text{ }j}}]}_{2\times 3}}\]
So, the elements in a
\[2\text{ }\times \text{ }3\]
matrix are
\[{{a}_{11}},\text{ }{{a}_{12}},\text{ }{{a}_{13}},\text{ }{{a}_{21}},\text{ }{{a}_{22}},\text{ }{{a}_{23}}\]
Let
\[A\text{ }=\text{ }{{[{{a}_{i\text{ }j}}]}_{2\times 3}}\]
So, the elements in a
\[2\text{ }\times \text{ }3\]
matrix are
\[{{a}_{11}},\text{ }{{a}_{12}},\text{ }{{a}_{13}},\text{ }{{a}_{21}},\text{ }{{a}_{22}},\text{ }{{a}_{23}}\]
\[{{a}_{11}}~=\]
\[{{a}_{12}}~=\]
\[{{a}_{13}}~=\]
\[{{a}_{21}}~=\]
\[{{a}_{22}}~=\]
\[{{a}_{23}}=\]
Substituting these values in matrix A we get,
