Linear Transformations: Example Problems

Please help. I always have a hard time with Linear Algebra. What's the difference between mapping from R3 into R2 and mapping from R2 into R3?

Why is the following not a linear transformation from R3 into R2?
L(x) = (1 + x1, x2)^T

And why is this one not a linear transformation from R2 into R3?
L(x) = (x1, x2, 1)^T


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...>R2, each input is in R3 and has the form (x1,x2,x3). The output is in R2 and has the form (y1,y2).
For ...