Home /
Expert Answers /
Other Math /
8-points-suppose-we-have-a-transformation-t-of-the-plane-it-satisfies-the-following-crite-pa121

(8 points) Suppose we have a transformation \( T \) of the plane. It satisfies the following criteria: - \( T\left[\begin{array}{l}1 \\ 2\end{array}\right]=\left[\begin{array}{l}1 \\ 2\end{array}\right] \) - \( T\left[\begin{array}{c}-2 \\ 1\end{array}\right]=\left[\begin{array}{c}2 \\ -1\end{array}\right] \) (a) (6 points) Find the matrix associated to this transformation. To do this, write down a matrix with unknown entries and use the above conditions to find a system of equations that you can solve for the entries. (b) (2 points) How would you describe this transformation? Hint: draw a diagram of the vectors \( [1,2] \) and \( [-2,1] \), then think about what's happening to them under the transformation.

(a) We can see that ?={[12],[?21] }