Consider the following matrix A = cos 4 sin 4 sin 4

Consider the following matrix A =



cos π

4 sin π

4

− sin π

4 cos π

4



.

Calculate Ax for x = 
1 0 
and x = 
0 1 
.

a. Sketch the original vectors and the results of the vector product.

b. What is the relationship between the original vectors and the vectors you get after multiplying by A? What are you doing when you multiply these vectors by A?

c. Take some other two-dimensional vectors and multiply them by A. Does the same thing happen?