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## Homework Statement

Determine if the transformation T: [tex]R^2\rightarrow R^2[/tex] is linear if T(x, y)= (x+1, 2y)

## Homework Equations

1. T(u + v) = T(u) + T(v)

2. T(c*u) = cT(u)

3. T(0) = 0

## The Attempt at a Solution

(1). I'm not sure how to prove the first condition (additivity). Can anyone help?

(2). T(c x,c y) = (c x+1, c 2y) = c(x+1, 2y) =c T(x,y)

For some scalar c.

(3). In (2) if c=0

T(0 x,0 y) = (0 x+1, 0 2y) = 0(x+1, 2y) =0