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

[sara_87]

Homework Statement

I have to determine whether the following is a linear transformation

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

Homework Equations

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?

 

[HallsofIvy]

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.)

 

[ircdan]

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