Linear Algebra - How to get matrix form Ax.

[theBEAST]

Homework Statement

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?

 

[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?

 

[vela]

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