$4\mathrm{.}12.$ Let $T$:$R^3{R}^3$ be the linear transformation given by

$T(x,y,z)=(x+y,y+z,x+z).$

Let $C$ denote the unit cube in $R^3$ determined by the standard basis $e_1,e_2,e_3.$ Find the volume of the image parallelepiped $T(C)$ of $C$ under $T.$