1. Find the standard matrix defined by the linear transformation

T(x,y,z) = (x-2y, -2x-y+z,-z)

is it going to be $\displaystyle \left(\begin{array}{ccc}1&-2&0\\-2&-1&1\\0&0&-1\end{array}\right)$

2. Let $\displaystyle T_1$ be the linear transformation corresponding to a rotation by an angle of $\displaystyle \theta_1$ about the x axis in $\displaystyle R^3$ and Let $\displaystyle T_2$ be the linear transformation corresponding to a rotation by an angle of $\displaystyle \theta_2$ about the z axis in $\displaystyle R^3$

will the standard matrix be

$\displaystyle \left(\begin{array}{ccc}1&0&0\\0&cos \theta& -sin \theta\\0&sin \theta&cos \theta\end{array}\right)$

and

$\displaystyle \left(\begin{array}{ccc}cos \theta&-sin \theta&0\\sin \theta&cost \theta& 0\\0&0&1\end{array}\right)$

Am I right with the above answers?