Linear Transformation to Different Dimensions

Is the following transformation linear?
T: R^3 -> R^2 defined by T(x,y,z)=(x,y)

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... in terms of their components in R^3. So let X=(x1, x2, x3) and Y=(y1, y2, y3). Then,
T(X+Y)=T((x1, x2, x3)+(y1, y2, y3))=T(x1+y1, x2+y2, x3+y3)
Now apply T, which takes the first ...