Multiplication of matrices $$E$$ and $$F$$ is $$G.$$ Matrices $$E$$ and $$G$$ are
$$E = \left[ {\matrix{ {\cos \theta } & { - sin\theta } & 0 \cr {sin\theta } & {\cos \theta } & 0 \cr 0 & 0 & 1 \cr } } \right]$$ and $$G = \left[ {\matrix{ 1 & 0 & 0 \cr 0 & 1 & 0 \cr 0 & 0 & 1 \cr } } \right]$$
What is the matrix $$F?$$

Eigen values of a matrix $$S = \left[ {\matrix{ 3 & 2 \cr 2 & 3 \cr } } \right]$$ are $$5$$ and $$1.$$ What are the eigen values of the matrix $${S^2} = SS?$$

The solution of the differential equation $${{dy} \over {dx}} + 2xy = {e^{ - {x^2}}}\,\,$$ with $$y(0)=1$$ is

If point A is in equilibrium under the action of the applied forces, the values of tensions and T _AB and T_AC are respectively.