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FP1 Matrix Transformation: Would this be sufficient in gaining full marks if this wer

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: ImageUploadedByStudent Room1414629397.226101.jpg

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 :frown:

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

Posted from TSR Mobile
(edited 9 years ago)
I am not sure where your sin(2theta) and -cos(2theta) came from... but ignoring that you approached this the right way.
Reply 2
Original post by Mathlover123
I am not sure where your sin(2theta) and -cos(2theta) came from... but ignoring that you approached this the right way.


oops i forgot to erase it


Posted from TSR Mobile
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.
Reply 4
Sorry if you saw my previous deleted post. I misread the question so my advice was useless.
Reply 5
Original post by notnek
Sorry if you saw my previous deleted post. I misread the question so my advice was useless.

Nope I didn't :P
Nice avatar btw
Reply 6
Original post by Mathlover123
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.
Reply 8
Original post by Mathlover123
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 ._.

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