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Use Matrices for Transformation

Module by: Kenny M. Felder. E-mail the author

Summary: A teacher's guide to using matrices for transformation.

This is a fun day. No new math, just a cool application of the math we’ve seen.

The in-class assignment pretty well speaks for itself. It’s worth mentioning that, despite the very simplified and silly nature of this specific assignment, the underlying message—that matrices are used to transform images in computer graphics—is absolutely true.

Some students (good students) may question why the last column 0000 size 12{ left [ matrix { 0 {} ## 0 } right ]} {} is necessary in specifying Harpoona’s initial condition. The reason is this representation is not simply a list of all the corner points in a shape. Yes, each column represents a point. But the matrix is a set of instructions to the computer, to draw lines from this point to that point. Without the last column, Harpoona would be missing her hypotenuse.

Homework

Homework: “Homework: Using Matrices for Transformation.” Here we see a matrix that rotates any object by 300, counter-clockwise. The inverse matrix, of course, rotates clockwise. Hopefully they will discover all that for themselves. And hopefully most of them will realize why an inverse matrix always does the exact opposite of the original matrix, since if you do them one after the other, you end up back where you started.

Time for Another Test!

Our first test on matrices.

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