# Transformation Matrix Problem

by PrinceOfDarkness
Tags: matrix, transformation
 Sci Advisor HW Helper P: 2,002 The idea is that, since we use vectors to denote physical quantities and we want to manipulate the vectors with components relative to a coordinate system, it shouldn't matter how we choose such a coordinate system. And we want to switch (transform) a set of components wrt one coordinate system to another. That's what the transformation matrix does. Now suppose you have some vector $\vec A$ and you have two coordinate systems $O$ and $O'$. The origins coincide, but the axes of $O'$ are rotated with respect to $O$ (it's rotated 120 degrees about the axis in the (1,1,1) direction in $O$). The transformation matrix should tell you how to transform the components of the vector $\vec A$ in $O$, which are $(A_x,A_y,A_z)$ into the components wrt O': $(A_x',A_y',A_z')$. I hope that'll help you in understanding the question. You can already smell immediately that you'll need 3x3 matrix.