# Is T(x,y) = (x,0) a linear transformation

1. Jan 22, 2008

### sara_87

1. The problem statement, all variables and given/known data

I have to determine whether the following is a linear transformation

T(x,y)=(x,0)

2. Relevant equations

3. The attempt at a solution

again, let v=(v1, v2) and w=(w1,w2)

then, T(v+w)=T(v1+w1, v2+w2)=(v1+w1, 0)

and, T(v)+T(w)=(v1+w1, 0)
so the first condition holds.

AND:

let c be a constant:
T(cv)=T(cv1,cv2)=(cv1, 0)=c(v1,0)=cT(v)
so both conditions hold
therefore it's linear transformation
is that correct?

2. Jan 22, 2008

### HallsofIvy

Staff Emeritus
You haven't said what x and y are! If they are real numbers, that is that T is a function from R2 to R2, then yes, those are exactly what you need to show. (Of course, taking c= 0 in the second shows T(0)= 0 and taking c= -1 shows T(-v)= -T(v) which are required by not necessary to prove separately.)

3. Jan 22, 2008

### ircdan

yea it is

edit: nevermind listen to halls, you do need to be more precise with this kind of thing probably