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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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