Matrix transformations

[Nomvalt]

For the following transformations, where T: R²--> R², state what transformation T represents and determine the image of the equation .





Dilation by a factor of from the x-axis
Reflection in the x-axis
Dilation by a factor of 2 from the y axis
Translation by 3 units to the right and 1 unit down

The answer for the image is

For some strange reason I got which is obviously wrong.
I don't understand how you get from the image described by the matrix to the image as the equation above. Anybody out there willing to help?

[Blakhitman]

multiply both sides by 2 to get:



multiply both sides by negative one to get:



Then sub them back into original equation



then solve for y to get:





Divide both sides by negative 2:



  the rule of the image is:

hope it makes sense

[the.watchman]

Shortcut: You have AND

Sub into the second eqn instead of solving for y:



Then sub the first eqn in to get your answer, much easier than solving both eqns

[Juddinator]

Shortcut: You have AND

Sub into the second eqn instead of solving for y:



Then sub the first eqn in to get your answer, much easier than solving both eqns

yeah, that's awesomeness for ya in methods right there
good work watchman!

[Blakhitman]

Shortcut: You have AND

Sub into the second eqn instead of solving for y:



Then sub the first eqn in to get your answer, much easier than solving both eqns

What do you mean by "much easier than solving both equations"?

[the.watchman]

Shortcut: You have AND

Sub into the second eqn instead of solving for y:



Then sub the first eqn in to get your answer, much easier than solving both eqns

What do you mean by "much easier than solving both equations"?

I meant that with the two x'=... AND y'=... you wouldn't have to solve both of them for x and y and sub them in, just solve one instead. It shortens it by at least four or five steps

[Blakhitman]

Oh lol, didn't even realise you didn't solve both. Anyway the way I did it may seem long because I modified the post to show each step, but really you don't need those "four" steps when actually working out .

I'm not saying yours isn't faster...it's just not "that" much faster

[the.watchman]

Oh lol, didn't even realise you didn't solve both. Anyway the way I did it may seem long because I modified the post to show each step, but really you don't need those "four" steps when actually working out .

I'm not saying yours isn't faster...it's just not "that" much faster

Lol, not "that" much, but still is better in my opinion
Anyway, it doesn't matter, fairly minor thing