Is this is linear transformation?

  • Thread starter Jamin2112
  • Start date
  • #1
Jamin2112
986
12

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)
 

Answers and Replies

  • #2
Ryker
1,086
2
To determine whether this is linear, your buddy needs to check whether it preserves vector addition and scalar multiplication.
 

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