- #1
embury
- 6
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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:
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?
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?