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

Here, a_ 11 =(1+1)^2 2 =(2)^2 2 =4 2 =2, a_ 12 =(1+2)^2 2 =(3)^2 2 =9 2 a_ 21 =(2+1)^2 2 =(3)^2 2 =9 2 , a_ 22 =(2+2)^2 2 =(4)^2 2 =16 2 =8 So, the required matrix is 29 2 9 2 8 .

Construct a 2 2 matrix A = [ a _ ij ] whose elements a _ ij are g…

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Question

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

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Answer

Here,
$\text{a}_{11}=\frac{(1+1)^2}{2}=\frac{(2)^2}{2}=\frac{4}{2}=2,$ $\text{a}_{12}=\frac{(1+2)^2}{2}=\frac{(3)^2}{2}=\frac{9}{2}$
$\text{a}_{21}=\frac{(2+1)^2}{2}=\frac{(3)^2}{2}=\frac{9}{2},$ $\text{a}_{22}=\frac{(2+2)^2}{2}=\frac{(4)^2}{2}=\frac{16}{2}=8$
So, the required matrix is $\begin{bmatrix}2\frac{9}{2}\\\frac{9}{2}8\end{bmatrix}.$

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