## Chapter 01. Matrices, Vectors, and Vector Calculus

### Problem 03. Transformation Matrix

##### The problem asks you to

find a transformation matrix that satisfying some condition.

##### This problem gives (or assumes)

This matrix rotates a rectangular coordinate through an angle of 120 degrees about an axis making equal angles with the original one.

##### You should know about

1) Direction cosine 2) Transformation matrix

##### Solution

We can see the relation between the rotated and the original coordinates system. This picture shows that

So, the transformation matrix is

Therefore,

##### Reference

https://math.stackexchange.com/questions/1599561/determining-the-transformation-matrix-r?newreg=f85754c5968d4b7fae383aabe7bfd2a5