Linear transformation

  • #1
1,197
1
how would one find the inverse of the linear transformation:

[tex]y_1=4x_1-5x_2[/tex]
[tex]y_2=-3x_1+4x_2[/tex]

this was never taught in class, could someone give a little advice as how I would do this?

I know the answer has to be in the form of

[tex]x_1=ay_1+by_2[/tex]
[tex]x_2=cy_1+dy_2[/tex]

could someone explain this process?
 

Answers and Replies

  • #2
NateTG
Science Advisor
Homework Helper
2,450
6
You're solving the system of equations for [itex]x_1[/itex] and [itex]x_2[/itex].


One way to do it would be to solve the first equation for [itex]x_1[/itex] and then substitute into the second equation.

Another method would be to add the equations together using suitable coefficitents so that one of the [itex]x[/itex]'s is eliminated, and then solve for the other.

In principle, this should be no different than dealing with, for example:
[tex]9=4x_1-5x_2[/tex]
[tex]7=-3x_1+4x_2[/tex]
 
  • #3
2,076
2
Yet another way is to write the equations in matrix form. (Left) Multiply both sides by the inverse of the coefficient matrix.
 

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