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1. The problem statement, all variables and given/known data

I actually have two questions:

1) I have a linear transformation L and it is represented by a matrix A. I also have a vector w, and I want to find out if w gets "hit" by L - see "answer-part" for my approach, and please comment.

2) Does the vectors that span R^n have to be orthogonal and linearly independant or only linearly independant? And is this the same for a vector-space in R^n? Please see comments in "answer-part" as well.

3. The attempt at a solution

1) Can I just solve the system Ax=w? If it is consistent, w gets "hit" by L?

2) The reason why I ask is that e.g. in R^3, the three unit vectors are orthogonal and linearly independant. And I have worked with vector-spaces in R^n where the vectors that span the space are not orthogonal. So I am a little confused here.

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# Homework Help: Linear algebra - transformations

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