Construct a matrix A = [ a _ i j ]_ 3 2 whose elements aij isgive… - Vidyadip

Question

Construct a matrix $A =\left[ a _{ i j}\right]_{3 \times 2}$ whose elements aij isgiven by : $a _{ ij }=\frac{(i+j)^3}{5}$

✓

Answer

$
\begin{aligned}
& a _{ ij }=\frac{(i+j)^3}{5} \\
& \therefore a 11=\frac{(1+1)^3}{5}=\frac{2^3}{5}=\frac{8}{5}, a_{12}=\frac{(1+2)^3}{5}=\frac{3^3}{5}=\frac{27}{5} \\
& a _{21}=\frac{(2+1)^3}{5}=\frac{3^3}{5}=\frac{27}{5}, a_{22}=\frac{(2+2)^2}{5}=\frac{4^3}{5}=\frac{64}{5} \\
& a _{31}=\frac{(3+1)^3}{5}=\frac{4^3}{5}=\frac{64}{5}, a_{32}=\frac{(3+2)^2}{5}=\frac{5^3}{5}=\frac{125}{5} \\
& \therefore A =\left[\begin{array}{cc}
\frac{8}{5} & \frac{27}{5} \\
\frac{27}{5} & \frac{64}{5} \\
\frac{64}{5} & \frac{125}{5}
\end{array}\right] \\
& =\left[\begin{array}{cc}
8 & 27 \\
27 & 64 \\
64 & 125
\end{array}\right] .
\end{aligned}
$

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