Is F(x1, x2) = (x1, x2, 0) a linear transformation?

[Jamin2112]

Homework Statement

My buddy was asking me this question. It's from his linear algebra homework.

F: R² --> R³
F[(x₁ x₂)] = (x₁ x₂ 0)

Homework Equations

I can't remember the definition of "linear transformation." Hopefully it's not too complicated.

The Attempt at a Solution

I don't think you have a vector with 2 rows be transformed into a vector with 3 rows. However, (x₁ x₂ 0) really is just equal to (x₁ x₂), so we could have F(x)=Ix, where I is the identity matrix. (Right? I dunno. I haven't taken this class for quite some time)

 

[Ryker]

To determine whether this is linear, your buddy needs to check whether it preserves vector addition and scalar multiplication.