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Monthly Archives: May 2013
Linear Algebra and Its Applications, Exercise 2.6.4
Exercise 2.6.4. Consider the matrix This matrix will “stretch” vectors along the x axis, transforming the vector into the vector . Consider also the circle formed by all points for which . What shape is the curve created by transforming … Continue reading
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Linear Algebra and Its Applications, Exercise 2.6.3
Exercise 2.6.3. Suppose we form the product of 2 by 2 matrices representing 5 reflections and 8 rotations. Does that product matrix represent a reflection or a rotation? Answer: I’ll show a long way to the answer and then a … Continue reading
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A summary of the effects of rotations and reflections
This post summarizes the results of previous posts exploring the effects of the following sequences of linear transformations in the xy plane: a rotation followed by a rotation a reflection followed by a reflection a rotation followed by a reflection … Continue reading
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A reflection followed by a rotation is a reflection
In preparation for answering exercise 2.6.3 in Gilbert Strang’s Linear Algebra and Its Applications, Third Edition, I wanted to derive in detail the effect of a rotation followed by a rotation, a reflection followed by a reflection, a rotation followed … Continue reading
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