The Laplace transform of $$\,\left( {{t^2} - 2t} \right)\,u\left( {t - 1} \right)$$ is ______________.

The value of $$\,\,\,\int\limits_1^2 {{1 \over x}\,\,\,dx\,\,\,\,} $$ computed using simpson's rule with a step size of $$h=0.25$$ is

A set of linear equations is represented by the matrix equations $$Ax=b.$$ The necessary condition for the existence of a solution for this system is

$$A = \left[ {\matrix{ 2 & 0 & 0 & { - 1} \cr 0 & 1 & 0 & 0 \cr 0 & 0 & 3 & 0 \cr { - 1} & 0 & 0 & 4 \cr } } \right].$$ The sum of the eigen values of the matrix $$A$$ is