$(2)($Determinant and Neutral Stability Curve$)$: Determine the relationship between the

parameters $k,Le,R{a}_t$ and $R{a}_c$ for which the following set of equations has nontrivial solution

$c_1-({}^2+k^2)c_2=0$

$Le{c}_1-({}^2+k^2)c_3=0$

$-({}^2+k^2)c_1+R{a}_t{k}^2{c}_2+R{a}_c{k}^2{c}_3=0$

$[$Remark: This relation is called the neutral stability curve and defines the onset of convection

in a fluid layer heated from below. Here, $k$ is the wave number, Le is the Lewis number and

$R{a}_t,R{a}_c$ are the thermal and concentration Rayleigh numbers, respectively.$]$

$(2)($Determinant and Neutral Stability Curve$)$: Determine the relationship between the

parameters $k,Le,R{a}_t$ and $R{a}_c$ for which the following set of equations has nontrivial solution

$c_1-({}^2+k^2)c_2=0$

$Le{c}_1-({}^2+k^2)c_3=0$

$-({}^2+k^2)c_1+R{a}_t{k}^2{c}_2+R{a}_c{k}^2{c}_3=0$

$[$Remark: This relation is called the neutral stability curve and defines the onset of convection

in a fluid layer heated from below. Here, $k$ is the wave number, $Le$ is the Lewis number and

$R{a}_t,R{a}_c$ are the thermal and concentration Rayleigh numbers, respectively.$]$