Let T: R^2 -> R^2 be an orthogonal transformation and let A is an element of...

Let T: R^2 -> R^2 be an orthogonal transformation and let A is an element of R^(2x2) be the standard matrix of T. In a) and b) below, by rotation we mean "rotation of R^2 by some angle and the origin". By reflection, we mean "reflection of R^2 over some line through the origin".

a) Show that T is either a rotation or a reflection.

b) Show that every rotation is a composition of 2 reflections, and thus that T is a composition of at most 2 reflections.

Expert Solution

Colby Messinger answered 2 years ago

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