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?

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# Linear Transformation/Injective/Surjective

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