transformation matrix: give geometric description for...

[mathstresser]

Give a geometric description of the matrix transformation f: R^2 --> R^2 defined by f(u)= Au for the given matrix A.

a) \(\displaystyle \L A\, =\, \left[\, \begin{array}{rr}-1&0\\0&1\end{array}\, \right]\)

b) \(\displaystyle \L A\, =\, \left[\, \begin{array}{rr}0&-1\\1&0\end{array}\, \right]\)

I know that geometric matrices are:

. . .\(\displaystyle \L \left[\, \begin{array}{ccc}a&b&c\\b&d&e\\c&e&f\end{array}\, \right]\)

But that's all I know.
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Edited by stapel -- Reason for edit: formatting matrices.

 

[pka]

Matrix A transforms point (x,y) into point (-x,y).
Matrix B transforms point (x,y) into point (-y,x).

Now you do some graphing. Make several transformations with both matrices and separate graphs. Try to identify the geometric action of each matrix.