Given
![\[{{a}_{i\text{ }j}}~=\text{ }{{e}^{2ix}}~sin\text{ }x\text{ }j\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d7acedd6d6cccc743f4b82c4bf2ab9d3_l3.png "Rendered by QuickLaTeX.com")
Let
![\[A\text{ }=\text{ }{{[{{a}_{i\text{ }j}}]}_{2\times 2}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-caac5e17af3cfc9dab3af7e3d91d65ae_l3.png "Rendered by QuickLaTeX.com")
So, the elements in a
![\[2\text{ }\times \text{ }2\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-4e94b8e16fdfe139c6f4b029e274086a_l3.png "Rendered by QuickLaTeX.com")
matrix are
![\[{{a}_{11}},\text{ }{{a}_{12}},\text{ }{{a}_{21}},\text{ }{{a}_{22}},\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-ee858f38235ecfefeab92cca9dccb8d3_l3.png "Rendered by QuickLaTeX.com")
![\[{{a}_{11}}~=\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-3601e0f418e15488560307acc94f9220_l3.png "Rendered by QuickLaTeX.com")
![\[{{a}_{12}}~=\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-3c59c4383cfe6826f822eaa6ef8dc303_l3.png "Rendered by QuickLaTeX.com")
![\[{{a}_{21}}~=\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-51d54c16f22fb179846ad2656b1f8e95_l3.png "Rendered by QuickLaTeX.com")
![\[{{a}_{22}}~=\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f468ef902c01115b7373e8787ebad435_l3.png "Rendered by QuickLaTeX.com")
Substituting these values in matrix A we get,
Construct a 2 × 2 matrix A = [ai j] whose elements ai j are given by: ai j = e2ix sin x j
Construct a 2 × 2 matrix A = [ai j] whose elements ai j are given by: ai j = e2ix sin x j