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Geometric Transformations with Matrices

A series of three different activities exploring linear transformations of the plane by matrix multiplication and looking at commutativity in two different ways.

Activity 1 (pencils and paper): a simple picture
is to be copied into an oblique parallelogram.

Activity 2 : my software lets students put different values in a transform matrix and instantly see the effect. They try to find the correct matrices for a variety of given transformations.

3. [T5] is the matrix for translating (sliding)
2 units to the right. Use the calculator to
work out [T5]10 and [T5]50 and write them down.
What transformations would these represent?


What do you think [T5]500 would be?

Activity 3 : Students complete a worksheet on various aspects of matrix multiplication, exponentiation and commutativity. They use both computation with graphics calculators and their new-found geometric interpretations.