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Niles
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[SOLVED] Linear algebra - transformations
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.
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.
Homework Statement
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.
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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