SOLUTION: How does one show that an operator is invertible?

Algebra ->  College  -> Linear Algebra -> SOLUTION: How does one show that an operator is invertible?      Log On


   



Question 578689: How does one show that an operator is invertible?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
How does one show that an operator is invertible?
----
Let's say "a" is your operator.
---
You want it to operate on "b"
---
It gives you "c" as a result.
-----
Now assume you have an operator "d"
---
You want it to operate on "c" and it gives you "a".
===============
Do you see that "d" has undone what "b" did?
-------------------
That means "b" and "d" are inverse operators.
It also shows that "b" is invertible: it can be undone.
----------------------
Dressing and undressing are invertible.
Eating is not invertible.
==============================
Cheers,
Stan H.