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Prove that any linear transformation ? : R? → R? maps a line passing through the...

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Advance Math

Prove that any linear transformation ? : R? → R? maps a linepassing through the origin to either the zero vector or a linepassing through the origin. Generalize this for planes andhyperplanes. What are the images of these under lineartransformations?


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Consider a line passing through the origin in Itcan be written in the formThen applying on wehaveIf then which is the zero vector Else    See Answer
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