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September 4th, 2015, 04:35 AM   #1
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Transformation question

Hello,

If v=x-2y and u=2x-y, to what line will x=y transform in the u,v plane?

I don't understand how am I supposed to find the line in terms of u,v plane .

Thanks!
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September 4th, 2015, 06:11 AM   #2
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Quote:
Originally Posted by noobinmath View Post
Hello,

If v=x-2y and u=2x-y, to what line will x=y transform in the u,v plane?

I don't understand how am I supposed to find the line in terms of u,v plane .

Thanks!
It simply means x=y in form of u and v
1st take out the value of x and y
X=(2u-v)/3
Y=(u-2v)/3


Now x=y
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September 4th, 2015, 06:12 AM   #3
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Originally Posted by Yash Malik View Post
It simply means x=y in form of u and v
1st take out the value of x and y
X=(2u-v)/3
Y=(u-2v)/3


Now x=y
U=-v or
u+v=0
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September 4th, 2015, 06:36 AM   #4
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Thanks! This is really the anwer! But how did you find out so easily that x=(2u-v)/3 for example?
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September 4th, 2015, 06:50 AM   #5
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Practice makes a man perfect
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September 4th, 2015, 07:07 AM   #6
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Quote:
Originally Posted by noobinmath View Post
v=x-2y and u=2x-y
There are many ways to solve this for x and y. Probably the simplest way is to proceed like this:
$\displaystyle \left \{ \begin{matrix} v = x - 2y \\ u = 2x - y \end{matrix} \right .$

Multiply the top equation by 2 and the bottom equation by -1
$\displaystyle \left \{ \begin{matrix} 2v = 2x - 4y \\ -u = -2x + y \end{matrix} \right .$

Now add the two equations:
$\displaystyle (2v - u) = (2x - 2x) + (-4 + 1)y$

$\displaystyle 2y - u = -3y$

$\displaystyle y = \frac{1}{3} (u - 2v)$

You can do a similar thing with the original equations to get the expression for x, or you could put $\displaystyle y = \frac{1}{3} (u - 2v)$ into either of the original equations and solve for x.

-Dan
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September 4th, 2015, 07:08 AM   #7
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Haha I will try again I was just playing with these two equations for quite some time and didn't get to separate x and y! always ended up with x=y or 0=0 etc!!


edit: Thanks Dan!
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September 4th, 2015, 07:22 AM   #8
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Gd job Dan i am a bit lazy so i didn't show the complete steps
Btw plz solve my limits question
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