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 : $a _{ ij }=\frac{(i-j)^2}{5-i}$

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Answer

$
A =\left[a_{i j}\right]_{3 \times 2}=\left(\begin{array}{ll}
a_{11} & a_{12} \\
a_{21} & a_{22} \\
a_{31} & a_{32}
\end{array}\right)
$
Now, $a_{i j}=\frac{(i-j)^2}{5-i}$
$
\begin{aligned}
\therefore a_{11} & =\frac{(1-1)^2}{5-1}=\frac{0}{4}=0 \\
a_{12} & =\frac{(1-2)^2}{5-1}=\frac{1}{4}
\end{aligned}
$
$
\begin{aligned}
a_{21} & =\frac{(2-1)^2}{5-2}=\frac{1}{3} \\
a_{22} & =\frac{(2-2)^2}{5-2}=\frac{0}{3}=0 \\
a_{31} & =\frac{(3-1)^2}{5-3}=\frac{4}{2}=2 \\
a_{32} & =\frac{(3-2)^2}{5-3}=\frac{1}{2} \\
\therefore A & =\left[\begin{array}{cc}
0 & \frac{1}{4} \\
\frac{1}{3} & 0 \\
2 & \frac{1}{2}
\end{array}\right]
\end{aligned}
$

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