By using properties of determinants ,show that: \(\begin{vmatrix}0&a&-b\\-a&0&-c\\b&c&0\end{vmatrix}\)=0
We have,
△= \(\begin{vmatrix}0&a&-b\\-a&0&-c\\b&c&0\end{vmatrix}\)
Applying R1 \(\to\) cR1,we have
△=\(\frac{1}{c}\begin{vmatrix}0&ac&-bc\\-a&0&-c\\b&c&0\end{vmatrix}\)
Applying R11\(\to\) R1-bR2,we have
△=\(\frac{1}{c}\begin{vmatrix}ab&ac&0\\-a&0&-c\\b&c&0\end{vmatrix}\)
=\(\frac{1}{c}\begin{vmatrix}b&c&0\\-a&0&-c\\b&c&0\end{vmatrix}\)
Here, the two rows R1 and R3 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