$2\mathrm{.}1.$ Determine whether the following strain fields are possible in a continuous material:

$($a$)\left[\begin{array}{cc}c(x^2+y^2)& cxy\\ cxy& y^2\end{array}\right],$

$,($b$)\left[\begin{array}{cc}{c}_z(x^2+y^2)& cxyz\\ cxyz& y^{2}z\end{array}\right]$

Here $c$ is a small constant, and it is assumed that ${}_z={}_{xz}={}_{yz}=0.$