3. w v The reflection of throughvw Reflection is a linear transformation Find a matrix M such that M = v The reflection of through y = mxv

4. y = mx 1 m  sin = m  cos = 1 

5.  sin = m  cos = 1  M = the counterclockwise rotation of through 2 degrees   The first column of M

6. sin = m  cos = 1  90-  The second column of M M = the clockwise rotation of through 2( 90 - )degrees  90- 

7. For y = 2x,

8. y = 2x

9. y = mx The process of finding a matrix to REFLECT a vector through the line y = mx can be greatly simplified by choosing a different basis

10. y = mx Choose a different basis: {, }

11. y = mx The matrix relative to the basis {, } is T=+10 T=+0

12. The matrix relative to the basis {, } is