The system of equations

X+2y+3z=4

2x+3y+4z=5

$\mathrm{If}f,g\mathrm{and}h\mathrm{are}\mathrm{differentiable}\mathrm{functions}\mathrm{of}x\mathrm{and}△\left(x\right)=\left|\begin{array}{ccc}f& g& h\\ \left(xf\right)\text{'}& \left(xg\right)\text{'}& \left(xh\right)\text{'}\\ \left(x^{2}f\right)\text{'}\text{'}& \left(x^{2}g\right)\text{'}\text{'}& \left(x^{2}h\right)\text{'}\text{'}\end{array}\right|,\mathrm{then}△\text{'}\left(x\right)\mathrm{is}$

If $\omega$ is a cube root of unity and $\Delta =\left|\begin{array}{cc}1& 2\omega \\ \omega & {\omega }^2\end{array}\right|$, then ${\Delta }^2$ is equal to

If ${\Delta }_1=\left|\begin{array}{cc}1& 0\\ a& b\end{array}\right|$ and ${\Delta }_2=\left|\begin{array}{cc}1& 0\\ c& d\end{array}\right|$, then ${\Delta }_2{\Delta }_1$ is equal to

If $A_1,B_1,C_1....$ are respectively the co-factors of the elements $a_1,b_1,c_1....$ of the determinant $\Delta =\left|\begin{array}{ccc}{a}_1& b_1& c_1\\ a_2& b_2& c_2\\ a_3& b_3& c_3\end{array}\right|,$ then $\left|\begin{array}{cc}{B}_2& C_2\\ B_3& C_3\end{array}\right|=$

If the system of linear equation $x+2ay+az=0,x+3by+bz=0,x+4cy+cz=0$ has a non zero solution, then a, b, c

If A = $\left|\begin{array}{ccc}5& 6& 3\\ -4& 3& 2\\ -4& -7& 3\end{array}\right|,$ then cofactors of the elements of $2^{nd}$ row are

The system of equations $x+y+z=2,3x-y+2z=6$ and $3x+y+z=-18$ has