# Standard Matrix Question

• Feb 6th 2011, 01:24 PM
flaming
Standard Matrix Question
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?
• Feb 7th 2011, 02:15 AM
Ackbeet
1. Most important: your angles need to be subscripted. That is, the problem statement has $\displaystyle \theta_{1}$ and $\displaystyle \theta_{2},$ so that's what you'd better have.
2. It's considered better practice to use non-italicized function names: $\displaystyle \cos(\theta)$ is better than $\displaystyle cos(\theta).$
3. I would highly recommend ALWAYS putting parentheses around function arguments. I've been burned on that one before, and so rather than write in a way that people can understand, I would rather try to write in a way that no one can misunderstand. So I'd recommend writing trig functions this way: $\displaystyle \sin(\theta),$ etc.