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Basic properties of linear transformations

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A linear transformation maps 0 to 0.
A linear transformation of a linear combination is the linear combination of the linear transformation
A linear transformation is determined by its action on a basis.
Definition of how the action of a linear transformation on a basis extends to the whole space
The solutions of a homogeneous system are the pre-image (of 0) of a linear transformation.

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A linear transformation of a linear combination is the linear combination of the linear transformation

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