I am extremely confused when it comes to linearly transformations and am not sure I entirely understand the concept. I have the following assignment question:(adsbygoogle = window.adsbygoogle || []).push({});

Consider the 2x3 matrix

A=

1 1 1

0 1 1

as a linear transformation from R3 to R2.

a) Determine whether A is a injective (one-to-one) function.

b) Determine whether A is a surjective (onto) function.

For a) I said that we need to solve Ax=0 and the matrix then looks like:

1 1 1 : 0

0 1 1 : 0

Since x3 is a free variable A cannot be injective.

For b) I have the matrix:

1 1 1 : *

0 1 1 : *

(note that it doesn't matter what * is)

This matrix is consistent so the matrix A is surjective.

Am I understanding this question correctly?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Linear Transformation/Injective/Surjective

**Physics Forums | Science Articles, Homework Help, Discussion**