Construct a 2 3 matrix A = [a_ ij ] whose elements a_ ij are give by :a_ij= (i+j)^2 2

Here, a_ij= (i+j)^2 2 a_ 11 =(1+1)^2 2 =(2)^2 2 =4 2 =2, a_ 12 =(1+2)^2 2 =(3)^2 2 =9 2 , a_ 13 =(1+3)^2 2 =(4)^2 2 =16 2 =8 a_ 21 =(2+1)^2 2 =(3)^2 2 =9 2 , a_ 22 =(2+2)^2 2 =(4)^2 2 =16 2 =8 and a_ 23 =(2+3)^2 2 =(5)^2 2 =25 2 Required matrix = A= 2&9 2 &8 9 2 &8&25 2

Construct a 2 3 matrix A = [a_ ij ] whose elements a_ ij are give…

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Question

Construct a $2 \times 3$ matrix $A = [a_{ij}]$ whose elements $a_{ij}$ are give by $:\text{a}_\text{ij}=\frac{(\text{i}+\text{j})^2}{2}$

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Answer

Here,
$\text{a}_\text{ij}=\frac{(\text{i}+\text{j})^2}{2}$
$\text{a}_{11}=\frac{(1+1)^2}{2}=\frac{(2)^2}{2}=\frac{4}{2}=2,$ $\text{a}_{12}=\frac{(1+2)^2}{2}=\frac{(3)^2}{2}=\frac{9}{2},$ $\text{a}_{13}=\frac{(1+3)^2}{2}=\frac{(4)^2}{2}=\frac{16}{2}=8$
$\text{a}_{21}=\frac{(2+1)^2}{2}=\frac{(3)^2}{2}=\frac{9}{2},$ $\text{a}_{22}=\frac{(2+2)^2}{2}=\frac{(4)^2}{2}=\frac{16}{2}=8$ and $\text{a}_{23}=\frac{(2+3)^2}{2}=\frac{(5)^2}{2}=\frac{25}{2}$
Required matrix = $\text{A}=\begin{bmatrix}2&\frac{9}{2}&8\\\frac{9}{2}&8&\frac{25}{2}\end{bmatrix}$

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