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Construct a 4 × 3 matrix A = [ai j] whose elements ai j are given by: ai j = i

Given \[{{a}_{i\text{ }j}}~=\text{ }i\]

Let \[A\text{ }=\text{ }{{[{{a}_{i\text{ }j}}]}_{4\times 3}}\]

So, the elements in a \[4\text{ }\times \text{ }3\] matrix are

\[{{a}_{11}},\text{}{{a}_{12}},\text{ }{{a}_{13}},\text{}{{a}_{21}},\text{}{{a}_{22}},\text{ }{{a}_{23}},\text{}{{a}_{31,}}{{a}_{32,}}{{a}_{33,}}{{a}_{41,}}{{a}_{42,}}{{a}_{43}}\]

\[A\text{ }=\]
RD Sharma Solutions for Class 12 Maths Chapter 5 Image 125

\[{{a}_{11}}~=\text{ }1\]

\[{{a}_{12}}~=\text{ }1\]

\[{{a}_{13}}~=\text{ }1\]

\[{{a}_{21}}~=\text{ }2\]

\[{{a}_{22}}~=\text{ }2\]

\[{{a}_{23}}~=\text{ }2\]

\[{{a}_{31}}~=\text{ }3\]

\[{{a}_{32}}~=\text{ }3\]

\[{{a}_{33}}~=\text{ }3\]

\[{{a}_{41}}~=\text{ }4\]

\[{{a}_{42}}~=\text{ }4\]

\[{{a}_{43}}~=\text{ }4\]

Substituting these values in matrix A we get,

\[A\text{ }=\]