Prove that a composite transformation formed by two successive reflections in any two straight lines through the origin that are perpendicular is equivalent to performing a half-turn about the origin.
I did this:
I don't know if this is enough but I'm not sure if I should add anything else? The answer at the back of the book just completely ignores this whole question. I don't know how to present answer in these kind of questions
And sorry for this messy working I took ages figuring out a matrix for reflection in perpendicular line :P
edit: the title died - Would this be sufficient in gaining full marks if this were an exam question? the 2theta in first matrix is just a careless mistake I forgot to erase it when I figured out what perpendicular line was
There is a few other ways of doing it, but your way is concise and quite nice. Last year we had to prove it via geometrical methods which were a bit more annoying.
There is a few other ways of doing it, but your way is concise and quite nice. Last year we had to prove it via geometrical methods which were a bit more annoying.
Whats geometrical methods? Did you have to draw it or what
Its first year degree maths, but it pretty much involves drawing it out its basically proving your first assumption, that is that you can describe a reflection as a matrix.
Its first year degree maths, but it pretty much involves drawing it out its basically proving your first assumption, that is that you can describe a reflection as a matrix.
Oh, makes sense if the assumption was wrong but the final result works out using the assumption, then the whole thing is wrong as well I think I saw some explanation about the reflection matrix in the book but it was quite confusing ._.