Given in a vector space , define by Show that T is one-to-one if and only if is independent.
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Originally Posted by Scopur Given in a vector space , define by Show that T is one-to-one if and only if is independent. is a linear transformation. Therefore, is one-to-one if and only if if and only if
uhh.. 2nd part i get one and i have the answer to this but.. I don't quite understand onto as well as the kernel. 2. T is onto iff
Originally Posted by Scopur uhh.. 2nd part i get one and i have the answer to this but.. I don't quite understand onto as well as the kernel. 2. T is onto iff A linear transformation is onto iff for any we can find so that . It should be clear now how to finish the proof.
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