Construct a 3 × 2 matrix whose elements
Question:

Construct a 3 × 2 matrix whose elements are given by aij = ei.xsin jx

Solution:

Let A be a 3 x 2 matrix

Such that, aij = ei.xsin jx; where where 1 ≤ i ≤ 3; 1 ≤ j ≤ 2

So, the terms are given as

$a_{11}=e^{x} \sin x \quad a_{12}=e^{x} \sin 2 x$

$a_{21}=e^{2 x} \sin x \quad a_{22}=e^{2 x} \sin 2 x$

$a_{31}=e^{3 x} \sin x \quad a_{32}=e^{3 x} \sin 2 x$

Therefore, $A=\left[\begin{array}{ll}e^{x} \sin x & e^{x} \sin 2 x \\ e^{2 x} \sin x & e^{2 x} \sin 2 x \\ e^{3 x} \sin x & e^{3 x} \sin 2 x\end{array}\right]$