Gujarat BoardEnglish MediumSTD 12 ScienceMathsMatrices1 Mark
Question
Construct a 2 $\times$ 2 matrix A = [aij], whose element aij = $\frac{(i+2j)^{2}}{2}$.
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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 $A\left[\begin{array}{ll} a_{11} & a_{12} \\ a_{21} & a_{22} \end{array}\right]=\left[\begin{array}{cc} \frac{9}{2} & \frac{25}{2} \\ 8 & 18 \end{array}\right]$
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