Math Is Fun Forum

dellatorre

Member

Registered: 2009-12-03

Posts: 2

Please Help with Matrices, Reflections, Rotations

Looking for help with a problem I'm working on:

"Show that matrix
[0 -1 0]
[-1 0 0]
[0 0 1]
for a reflection about line y=-x
is equivalent to a reflection relative to the y axis followed by a counter-clockwise rotation of 90 degrees."

So for my answer, first I have for the reflection relative to the y axis, I have the matrix:
[-1 0 0]
[0 1 0]
[0 0 1]

and for the counter-clockwise rotation of 90 degrees, I have the matrix:
[0 -1 0]
[1 0 0]
[0 0 1]

but then I don't know what my next step should be.

Can anyone help me with this?

thanks,
Della

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Please Help with Matrices, Reflections, Rotations

To do one transformation and then the other is composing the transformations.  For example, to apply f and then g we do g(f(x)).  For matrices, composition of linear transformations is given by matrix multiplication.  But remember, order is important.  So which matrix goes on the left, and which goes on the right?

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

dellatorre

Member

Registered: 2009-12-03

Posts: 2

Re: Please Help with Matrices, Reflections, Rotations

thank you