Question
Construct a matrix $A=\left[a_{i j}\right]_{3 \times 2}$ whose elements ay are given by
$a_{i j}=\frac{(i+j)^3}{5}$
$a_{i j}=\frac{(i+j)^3}{5}$
$\therefore \quad a_{11}=\frac{(1+1)^3}{5}=\frac{2^3}{5}=\frac{8}{5}, a_{12}=\frac{(1+2)^3}{5}=\frac{3^3}{5}=\frac{27}{5}$
$\begin{aligned} & a_{21}=\frac{(2+1)^3}{5}=\frac{3^3}{5}=\frac{27}{5}, a_{22}=\frac{(2+2)^3}{5}=\frac{4^3}{5}=\frac{64}{5} \\ & a_{31}=\frac{(3+1)^3}{5}=\frac{4^3}{5}=\frac{64}{5}, a_{32}=\frac{(3+2)^3}{5}=\frac{5^3}{5}=\frac{125}{5}\end{aligned}$
$\therefore \quad A=\left[\begin{array}{cc}\frac{8}{5} & \frac{27}{5} \\ \frac{27}{5} & \frac{64}{5} \\ \frac{64}{5} & \frac{125}{5}\end{array}\right]=\frac{1}{5}\left[\begin{array}{cc}8 & 27 \\ 27 & 64 \\ 64 & 125\end{array}\right]$
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f(x) = $\frac{x^2 +18x-19}{x-1}$for x ≠ 1
= 20, for x = 1, at x = 1.