Question

determine if function T: R^2 --> R^2 are one to one or onto

T(x,y)=(2x,y)

Answer 1

is there any more info on this?

Answer 2

nope, that is it..

Answer 3

what is the name of the section this is out of form your textbook?

Answer 4

geometry of maps from R2 to R2, vector calc.

Answer 5

this function is one one onto

Answer 6

oooohh.... ok, when you say R^2 you mean mapping from R2 to R2.
its easier than what were making it out to be

Answer 7

what do i do to know if it is one to one or onto.

Answer 8

yeah like 2d

Answer 9

does your textbook have a section on "one to one" vectors?

Answer 10

let \(\vec x\) = (x,y)

T(\(\vec x\)) = A\(\vec x\)

\[\begin{pmatrix}2&0\\0&1\end{pmatrix}\binom{x}{y}=\binom{2x}{y}\]

Answer 11

okay so you put a derivative in a determinant ?

Answer 12

not a derivative :) i made a matrix A that transforms any given input (x,y) and produces an output (2x,y)

Answer 13

the mapping is one to one if every input has a unique output.

can we create an inverse of this? so that for every 2x,y, we can get back to x,y ?

Answer 14

not sure ?

Answer 15

\[\begin{pmatrix}\frac 12&0\\0&1\end{pmatrix}\binom{2x}{y}=\binom{x}{y}\]

Answer 16

if you are not familiar with matrixes ... then none of this will make sense

Answer 17

...none of it makes sense. haha. the book is saying that if it is one to one if T(u,v) = T(u',v')

Answer 18

im not sure that ' denotes a derivative in this case