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The operation of mutiplying a vector by a constant matrix can by thought of as transforming a point in space onto another point in space.
Below are ten questions about the properties of such transformations in three dimensions for you to think about. There are some hints and suggestions in the Getting Started section.
As you think about the questions, can you draw relevant diagrams and construct relevant algebraic examples? In each case, is there a definitive answer, or does it depend on various factors? You may intuitively feel the answers to some of these questions; in these cases can you prove your intuition correct?
There are more matrix problems in this feature.