Construct a 2 × 2 matrix A = [aij] whose elements aij are given b… - Vidyadip

Question

Construct a 2 × 2 matrix A = [a_ij] whose elements a_ij are given by:
$\text{a}_\text{ij}=\frac{|-3\text{i}-\text{j}|}{2}$

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Answer

Here,
$\text{a}_{11}=\frac{|-3(1)+1|}{2}=\frac{|-3+1|}{2}=\frac{|-2|}{2}=1,$ $\text{a}_{12}=\frac{|-3(1)+2|}{2}=\frac{|-3+2|}{2}=\frac{|-1|}{2}=\frac{1}{2}$
$\text{a}_{21}=\frac{|-3(2)+1|}{2}=\frac{|-6+1|}{2}=\frac{|-5|}{2}=\frac{5}{2},$ $\text{a}_{22}=\frac{|-3(2)+2|}{2}=\frac{|-6+2|}{2}=\frac{|-4|}{2}=2$
So, the required matrix is $\begin{bmatrix}1&\frac{1}{2}\\\frac{5}{2}&2\end{bmatrix}.$

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