A system matrix is given as follows $$$A = \left[ {\matrix{ 0 & 1 & { - 1} \cr { - 6} & { - 11} & 6 \cr { - 6} & { - 11} & 5 \cr } } \right].$$$

The absolute value of the ratio of the maximum eigenvalue to the minimum eigenvalue is ___________.

Let $$f\left( x \right) = x{e^{ - x}}.$$ The maximum value of the function in the interval $$\left( {0,\infty } \right)$$ is

The line integral of function $$F=yzi,$$ in the counterclockwise direction, along the circle $${x^2} + {y^2} = 1$$ at $$z=1$$ is

A fair coin is tossed $$n$$ times. The probability that the difference between the number of heads and tails is $$(n-3)$$ is