Question

construct a matrix A=[aij]2×3 whose element aij is given by aij=i2+j2/2​

Answer 1

$\large\underline{\sf{Solution-}}$

Let us consider a matrix of order 2 × 3 as

$\begin{gathered}\sf \rm :\longmapsto\:\:A=\left[\begin{array}{ccc}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\end{array}\right]\end{gathered}$

Now, it is given that

$\bf :\longmapsto\:a_{ij} \: = \: \dfrac{ {i}^{2} + {j}^{2} }{2}$

So,

$\bf :\longmapsto\:a_{11} \: = \: \dfrac{ {1}^{2} + {1}^{2} }{2} = 1$

$\bf :\longmapsto\:a_{12} \: = \: \dfrac{ {1}^{2} + {2}^{2} }{2} = \dfrac{1 + 4}{2} = \dfrac{5}{2}$

$\bf :\longmapsto\:a_{13} \: = \: \dfrac{ {1}^{2} + {3}^{2} }{2} = \dfrac{1 + 9}{2} = \dfrac{10}{2} = 5$

$\bf :\longmapsto\:a_{21} \: = \: \dfrac{ {2}^{2} + {1}^{2} }{2} = \dfrac{4 + 1}{2} = \dfrac{5}{2}$

$\bf :\longmapsto\:a_{22} \: = \: \dfrac{ {2}^{2} + {2}^{2} }{2} = \dfrac{4 + 4}{2} = \dfrac{8}{2} = 4$

$\bf :\longmapsto\:a_{23} \: = \: \dfrac{ {2}^{2} + {3}^{2} }{2} = \dfrac{4 + 9}{2} = \dfrac{13}{2}$

Hence, on substituting all these values in above matrix, we get

$\begin{gathered}\sf \bf\implies \:\:A=\left[\begin{array}{ccc}1&\dfrac{5}{2} &5 \\ \\\dfrac{5}{2} &4&\dfrac{13}{2} \end{array}\right]\end{gathered}$