Linear Transformations

Experiment with the transformation where .

Move the vector in the plot on the left . You'll see move in the plot on the right.

Check that by moving to . Is on ?

(Q1) Now compute by moving to . Answer:

Check that sends to by moving to . Is on ?

(Q2) Where does send the vector ?

Suppose that for the matrix you want to solve .

The old way of thinking about this problem would be to row reduce .

The new way of thinking about this problem asks you to find the that sends to .

Here's the same picture of with added.

Move the vector until you find the that sends to .

If you found the answer , then you've opened your mind up to a whole new way of solving .

Here's the same picture of with added.

(Q3) Use the graphic to find that solves .

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Copyright © 2007 Todd Will

Created by
Mathematica (April 15, 2007)