Question

Find the matrix aa representing the reflection about the line ll in r2r2 which consists of all scalar multiples of the vector [45][45].

Answer 1

 All scalar multiples of the vector [ 4, 5] makes the line y = 5/4 x. 

The matrix A of the orthogonal projection onto the line L is made of the coordinates of the projections of the base trajectories i and j onto the line L printed in columns. 

The line L: y = 5/4*x 

Orthogonal line passing over the point (1, 0): y = -4/5 *x + 4/5

Point of Intersection: (16/41, 21/41) 

Projections: P(i) = 16/41 i + 21/41 j, P(j) = 16/41 i + 21/41 j 

The matrix: 

A = || 16/41..16/41|| 
......|| 16/41....16/41 ||