Let T be the reflection about the line 6x3y0 in the euclidea

Let T be the reflection about the line 6x+3y=0 in the euclidean plane. The standard matrix A of T is

A has 2 eigenvalues. One of them is and its corresponding eigenspace is

The other eigenvalue of A is and its corresponding eigenspace is

Hint: Use geometric reasoning!

Solution

Solution:   Given line equation, 6x = -3y

                 this can be resolved as y = -2x

                 The slope of this line is -2 and hence the line relected to this line will be with slope of +2

                 The line equation will be y = 2x