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

y = mx 1 m  sin = m  cos = 1 

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

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

For y = 2x,

y = 2x

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

y = mx Choose a different basis: {, }

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

The matrix relative to the basis {, } is