Independent Controls

Here's the picture of xA x for another 2  2 matrix A.

Like before you control x on the left and A x responds on the right.
This time you control the two coordinates of x independently.
Use the red point to control horizontal movement.
Use the blue point to control vertical movement.

The vector y appears in the plot on the right.  
Use the graphic to find x that solves A x = y.

Here's the same picture of xA x , but now you see where the matrix A sends the grid in the left plot. 

The matrix A sends the grid in the left plot to a slanted grid in the right plot.
The grid makes it easier to find that x = (1 )        -3 is the solution to A x = y .

Here's the same picture of xA x with y = (-4)        3 added.

(Q4) Solve A x = (-4)         3.


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Copyright 2007 Todd Will
Created by Mathematica  (April 15, 2007)