Construct a 2 2 matrix A = [a_ ij ], whose element a_ ij = (i+2j)^ 2 2 .

Since it is a 2 2 matrix it has 2 rows and 2 column. Let matrix be A Where A= [ ll a_ 11 & a_ 12 a_ 21 & a_ 22 ] Now it is given that a_ ij = (i+2 j)^2 2 a_ 11 =(1+2(1))^2 2 =(1+2)^2 2 =(3)^2 2 =9 2 a_ 12 =(1+2(2))^2 2 =(1+4)^2 2 =(5)^2 2 =25 2 a_ 21 =(2+2(1))^2 2 =(2+2)^2 2 =(4)^2 2 =16 2 = 8 a_ 22 =(2+2(2))^2 2 =(2+4)^2 2 =(6)^2 2 =36 2 = 18 Hence, the required matrix A is A [ ll a_ 11 & a_ 12 a_ 21 & a_ 22 ]= [ cc 9 2 & 25 2 8 & 18 ]

Construct a 2 2 matrix A = [a_ ij ], whose element a_ ij = (i+2j)…

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Question

Construct a $2 \times 2$ matrix $A = [a_{ij}],$ whose element $a_{ij} = \frac{(i+2j)^{2}}{2}$.

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Answer

Since it is a $2 \times 2$ matrix
it has $2$ rows and $2$ column.
Let matrix be $A$
Where $A=\left[\begin{array}{ll} a_{11} & a_{12} \\ a_{21} & a_{22} \end{array}\right]$
Now it is given that
$\mathrm{a}_{\mathrm{ij}}=\frac{(\mathrm{i}+2 \mathrm{j})^2}{2}$
$a_{11}=\frac{(1+2(1))^2}{2}=\frac{(1+2)^2}{2}=\frac{(3)^2}{2}=\frac{9}{2}$
$a_{12}=\frac{(1+2(2))^2}{2}=\frac{(1+4)^2}{2}=\frac{(5)^2}{2}=\frac{25}{2}$
$\mathrm{a}_{21}=\frac{(2+2(1))^2}{2}=\frac{(2+2)^2}{2}=\frac{(4)^2}{2}=\frac{16}{2}$ = 8
$\mathrm{a}_{22}=\frac{(2+2(2))^2}{2}=\frac{(2+4)^2}{2}=\frac{(6)^2}{2}=\frac{36}{2}$ = 18
Hence,
the required matrix $A$ is
$A\left[\begin{array}{ll} a_{11} & a_{12} \\ a_{21} & a_{22} \end{array}\right]=\left[\begin{array}{cc} \frac{9}{2} & \frac{25}{2} \\ 8 & 18 \end{array}\right]$