Question: 24. Prove that if' T . { - #` is a one - to- one linear transformation and S' = (VI , I' ] .

24. Prove that if' T . {" - #` is a one - to- one linear transformation and S' = (VI , I' ] . .... It' is a set of linearly independent vectors from # ", then ( TIVI ) , TIVE) . .... TIVE'!' is a set of linearly independent vectors from ` Hint . Begin the proof by considering the dependence test equation : [ I'll vi ) + [ ] ( " ; ) + ... + CT ( VA ) = 1` Rewrite the left side using the linearity properties of' I' and use the Kernel Test for Injectivity

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