Construct a 3 × 2 matrix whose elements are given by a_ ij =e^ i.… - Vidyadip

Question

Construct a 3 × 2 matrix whose elements are given by $\text{a}_{\text{ij}}=\text{e}^{\text{i.x}}=\sin\text{jx}.$

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Answer

We have, $\text{A}=[\text{a}_{\text{ij}}]_{3\times2},$

Such that, $\text{a}_{\text{ij}}=\text{e}^{\text{i.x}}=\sin\text{jx};$ where $1\leq\text{i}\leq3$ and $1\leq\text{j}\leq2,\ \text{i, j}\in\text{N}$

$\therefore\ \text{a}_{11}=\text{e}^\text{x}\sin\text{x}$	$\text{a}_{12}=\text{e}^{\text{x}}\sin2\text{x}$
$\text{a}_{21}=\text{e}^{2\text{x}}\sin\text{x}$	$\text{a}_{22}=\text{e}^{2\text{x}}\sin2\text{x}$
$\text{a}_{31}=\text{e}^{3\text{x}}\sin\text{x}$	$\text{a}_{32}=\text{e}^{3\text{x}}\sin2\text{x}$

$\therefore\ \text{A}=\begin{bmatrix}\text{e}^{\text{x}}\sin\text{x}&\text{e}^{\text{x}}\sin2\text{x}\\\text{e}^{2\text{x}}\sin\text{x}&\text{e}^{2\text{x}}\sin2\text{x}\\\text{e}^{3\text{x}}\sin\text{x}&\text{e}^{3\text{x}}\sin2\text{x}\end{bmatrix}$

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