1. ## Transformations of Variables

I need to find the image of a line under a specific operator, but there are 4 variables, two of which are direct results of a transformation.

Suppose that T maps (x,y) into (s,t) is the linear operator on R2 defined by the equations:
2x+y=s
6x+2y=t

Find the image of the line x+y=1 under this operator.

Well, I know that the standard matrix is
2 1
6 2

but how do I find the image of x+y=1?

2. Originally Posted by Hellreaver
I need to find the image of a line under a specific operator, but there are 4 variables, two of which are direct results of a transformation.

Suppose that T maps (x,y) into (s,t) is the linear operator on R2 defined by the equations:
2x+y=s
6x+2y=t

Find the image of the line x+y=1 under this operator.

Well, I know that the standard matrix is
2 1
6 2

but how do I find the image of x+y=1?
$y = 3s - t$
$x = -s + \frac{1}{2} t$

3. How did you get that? It looks like you divided by 2 somewhere, but I'm not sure...

4. Originally Posted by Hellreaver
How did you get that? It looks like you divided by 2 somewhere, but I'm not sure...
I treated

2x+y=s
6x+2y=t

as simultaneous equations and solved for x and y in terms of s and t.

5. Oh, ok, I see what you did... Now would I have to put those values into x+y=1?

6. Originally Posted by Hellreaver
Oh, ok, I see what you did... Now would I have to put those values into x+y=1?
Well I sure didn't find them because they'd look pretty on the mantlepiece ......