The following four vector fields are given in cartesian coordinate system. The vector field which does not satisfy the property of magnetic flux density is

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 ___________.

Given a system of equations $$$x + 2y + 2z = {b_1}$$$ $$$5x + y + 3z = {b_2}$$$
Which of the following is true its solutions

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