Using the property of determinants and without expanding, prove that: \(\begin{vmatrix}2&7&65\\3&8&75\\5&9&86\end{vmatrix}\)=0
\(\begin{vmatrix}2&7&65\\3&8&75\\5&9&86\end{vmatrix}\)
=\(\begin{vmatrix}2&7&63+2\\3&8&72+3\\5&9&81+5\end{vmatrix}\)
=\(\begin{vmatrix}2&7&63\\3&8&72\\5&9&81\end{vmatrix}+\begin{vmatrix}2&7&2\\3&8&3\\5&9&5\end{vmatrix}\)
=\(\begin{vmatrix}2&7&9(7)\\3&8&9(8)\\5&9&9(9)\end{vmatrix}+0\) [Two columns are identical]
=\(9\begin{vmatrix}2&7&7\\3&8&8\\5&9&9\end{vmatrix}\) [Two columns are identical]
=0
A settling chamber is used for the removal of discrete particulate matter from air with the following conditions. Horizontal velocity of air = 0.2 m/s; Temperature of air stream = 77°C; Specific gravity of particle to be removed = 2.65; Chamber length = 12 m; Chamber height = 2 m; Viscosity of air at 77°C = 2.1 × 10\(^{-5}\) kg/m·s; Acceleration due to gravity (g) = 9.81 m/s²; Density of air at 77°C = 1.0 kg/m³; Assume the density of water as 1000 kg/m³ and Laminar condition exists in the chamber.
The minimum size of particle that will be removed with 100% efficiency in the settling chamber (in $\mu$m is .......... (round off to one decimal place).
Read More: Properties of Determinants