Construct a 3 - 2 matrix whose elements are given by a ij - e i - x sin jx-

Since, A=[a_ij]_m× n1≤ i≤ m and 1≤ j≤ n, i. j ϵ N A=[e^i.xsin jx]_3× 2:1≤ i≤ 3;1≤ j≤ 2 ⇒ a_11=e^1.x.sin1.x=e^x sin x a_12=e^1.x,sin 2.x=e^x sin2x a_21=e^2.x. ...

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Standard XII

Mathematics

Logarithmic Differentiation

Construct a 3...

Question

Construct a 3 $\times$ 2 matrix whose elements are given by $a_{i j} = e^{i . x}$ sin jx.

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Solution

Since, $A = [a_{i j}]_{m \times n} 1 \leq i \leq m a n d 1 \leq j \leq n, i . j ϵ N$
$A = [e^{i . x} s i n j x]_{3 \times 2} : 1 \leq i \leq 3; 1 \leq j \leq 2$
$\Rightarrow a_{11} = e^{1. x} . s i n 1. x = e^{x} s i n x$
$a_{12} = e^{1. x}, s i n 2. x = e^{x} s i n 2 x$
$a_{21} = e^{2. x} . s i n 1. x = e^{2 x} s i n x$
$a_{22} = e^{2. x} . s i n 2. x = e^{2 x} s i n 2 x$
$a_{31} = e^{3. x} . s i n 1. x = e^{3 x} s i n x$
$a_{32} = e^{3. x} . s i n 2. x = e^{3 x} s i n 2 x$

$∴ A = {⎡ ⎢ ⎣ \begin{matrix} e^{x} s i n x e^{x} s i n 2 x e^{2 x} s i n x e^{2 x} s i n 2 x e^{3 x} s i n x e^{3 x} s i n 2 x \end{matrix} ⎤ ⎥ ⎦}_{3 \times 2}$

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

Construct a 3 $\times$ 2 matrix whose elements are given by $a_{i j} = e^{i . x}$ sin jx.