Hey guys,

I was revising Linear Transformation and I came accross a couple of doubts here and there. Hope you guys would be able to explain to me for me to understand it better (:

1. I know how to attempt questions with two variables, eg. S(x,y) = (2x-y, x+y) to prove that they are linear transformations. What is the method to attempt those with three variables involved? eg. T(x,y,z) = (0, 2x+y) or F(x,y,z) =

2. What is the way to see the transformation patterns ? eg. is the reflection of y = x. Say, how do we determine what is the transformation for a matrix like or , etc.

3. Whats the meaning of surjective & injective?

4. I was taught how to tackle most of the questions in matrix form. When it comes to polynomial, I'd go nuts figuring how to attempt the question Especially when it comes to change of basis questions. Like what is [T]s and things like that when from matrix you can find it as the matrix representation.

eg. T[p(x)] = p(2x+1), B = {1, x, x^2}

Find [T]B.

Thanks for your timeeee!