If $A = [a_{i j}], i, j = 1, 2$ where $a_{i j}$ is defined as $a_{i j} = i^{2} + j^{2}$ then write the sum of the elements of the matrix $A$

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Solution

$A = [a_{i j}] i, j = 1, 2, a_{i j} = i^{2} + j^{2}$
Now, $a_{11} = {(1)}^{2} + {(1)}^{2} = 1 + 1 = 2$
$a_{12} = {(1)}^{2} + {(2)}^{2} = 1 + 4 = 5$
$a_{21} = {(2)}^{2} + {(1)}^{2} = 4 + 1 = 5$
$a_{22} = {(2)}^{2} + {(2)}^{2} = 4 + 4 = 8$
$∴$ Matrix $A = [\begin{matrix} a_{11} & a_{12} a_{21} & a_{22} \end{matrix}]$
$A = [\begin{matrix} 2 & 5 5 & 8 \end{matrix}]$
Sum of elements is $20$ .

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