I was watching 3b1b video on linear transformations.
In that he said that linear transformations of matrices preserves origin from the original space to transformed space.
Now I got to prove this fact from the property of linearity:
$T(v+w)=T(v) + T(w) and T(cv) = cT(v)$ But then thinking of a straight line as linear transformation of $x$ to $y$ using $y=mx+c$
I think we call it a linear equation. And as transformation is a function really, thus the function $f(x)=mx+c$ is a linear function.
But I am not getting the property of linearity satisfied here. For example,
$f(x) = mx+c$
when x=0, $f(0)= c$, thus O from original space is not mapped to 0 in transformed space.
Also, $f(0+5) = 5(x+0)+c = 5x+c $ but $f(0) + f(5) = c + 5x + c $.
Thus I am getting the linearity not satisfying. Is $y=mx+c$ not a linear transformation?
Thank you !