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

Here, a_ 11 =[1-2(1)]^2 2 =(1-2)^2 2 =(-1)^2 2 =1 2 , a_ 12 =[1-2(2)]^2 2 =(1-4)^2 2 =(-3)^2 2 =9 2 a_ 21 =[2-2(1)]^2 2 =(2-2)^2 2 =0 2 =0, a_ 22 =[2-2(2)]^2 2 =(2-4)^2 2 =(-2)^2 2 =4 2 =2 So, the required matrix is 1 2 &9 2 0&2 .

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

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Question

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

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Answer

Here,
$\text{a}_{11}=\frac{[1-2(1)]^2}{2}=\frac{(1-2)^2}{2}=\frac{(-1)^2}{2}=\frac{1}{2},$ $\text{a}_{12}=\frac{[1-2(2)]^2}{2}=\frac{(1-4)^2}{2}=\frac{(-3)^2}{2}=\frac{9}{2}$
$\text{a}_{21}=\frac{[2-2(1)]^2}{2}=\frac{(2-2)^2}{2}=\frac{0}{2}=0,$ $\text{a}_{22}=\frac{[2-2(2)]^2}{2}=\frac{(2-4)^2}{2}=\frac{(-2)^2}{2}=\frac{4}{2}=2$
So, the required matrix is $\begin{bmatrix}\frac{1}{2}&\frac{9}{2}\\0&2\end{bmatrix}.$

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