# Homework Help: Linear Algebra - How to get matrix form Ax.

1. Feb 22, 2012

### theBEAST

1. The problem statement, all variables and given/known data
I know the title is misleading but what I am asking is how I can get this matrix
x1cosθ-x2sinθ
x1sinθ+x2cosθ

to the matrix multiplication form
cosθ -sinθ | x1
sinθ cosθ | x2

where
A=
cosθ -sinθ
sinθ cosθ
x=
x1
x2

Is there a good method to do this or do I have to find it by eye-balling it?

2. Feb 22, 2012

### Deveno

have you tried perfoming the matrix multiplication:

$$\begin{bmatrix}\cos\theta&-\sin\theta\\ \sin\theta&\cos\theta\end{bmatrix}\begin{bmatrix}x_1\\x_2\end{bmatrix} = ?$$

and comparing that to what you want?

3. Feb 22, 2012

### vela

Staff Emeritus
What's the usual way of finding the columns of the matrix representing a linear transformation? It should be mentioned in your book somewhere.