The general solution of $\frac{d^2 y}{d x^2}-6 \frac{d y}{d x}+9 y=0$ is

The partial derivative of the function

$$ f(x, y, z)=e^{1-x \cos y}+x z e^{\frac{-1}{\left(1+y^2\right)}} $$

with respect to $x$ at the point $(1,0, e)$ is

For a vector field $\vec{A}$, which one of the following is FALSE?

Consider the following system of linear equations.

$$ x_1+2 x_2=b_1 ; 2 x_1+4 x_2=b_2 ; 3 x_1+7 x_2=b_3 ; 3 x_1+9 x_2=b_4 $$

Which one of the following conditions ensures that a solution exists for the above system?