5) Let T: R2 → R2 reflection (or orthogonal symmetry) with respect to the line 2x - y = 0. We call back that the vector a = (). is orthogonal to the line in question and the vector b = (G) is on this...

Extracted text: 5) Let T: R2 → R2 reflection (or orthogonal symmetry) with respect to the line 2x - y = 0. We call back that the vector a = (). is orthogonal to the line in question and the vector b = (G) is on this line, a) Give T (a) and T (b) (think about the geometry of reflection) b) Give the canonical matrix of T. Hint: use a) and an inverse matrix c) Express the vector e = as a linear combination of a and b and using linearity of T, give T (e1). Do the same with d) Using c), find the canonical matrix of T and give the vector obtained by the reflection of the vector (3) in relation to the line in question.