Confusion about properties of linear transformation. I learned from 3Blue1Brown's Linear Algebra

persepsi1ea

persepsi1ea

Answered question

2022-02-15

Confusion about properties of linear transformation.
I learned from 3Blue1Brown's Linear Algebra videos that one of the rules for a transformation to be linear is that the origin remains fixed in place after transformation. So if T(x)=x+a is a given transformation, I know that by inserting x=0, it is not a linear transformation. I am not able to understand what is non-linear about it.

Answer & Explanation

Layla Humphrey

Layla Humphrey

Beginner2022-02-16Added 11 answers

Because T(0+0)=a, whereas T(0)+T(0)=2a, which is different from a (unless a=0, of course). But one should have T(0+0)=T(0)+T(0) if T was linear.
monogamab0f

monogamab0f

Beginner2022-02-17Added 9 answers

If a0,then T(0)0. The transformation is what we call affine, but not strictly linear.

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