$$\mathop {Lt}\limits_{x \to 0} {{{{\log }_e}\left( {1 + 4x} \right)} \over {{e^{3x}} - 1}}$$ is equal to

A real square matrix $$A$$ is called skew-symmetric if

The number of linear independent eigenvectors of matrix $$A = \left[ {\matrix{ 2 & 1 & 0 \cr 0 & 2 & 0 \cr 0 & 0 & 3 \cr } } \right]$$ is ________.

$$\mathop {Lt}\limits_{x \to \infty } \left( {\sqrt {{x^2} + x - 1} - x} \right)$$ is