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# Prove that if T: Rn --> Rm is a one-to-one linear

24. Prove that if' T . {" - #` is a one - to- one linear transformation and S' = (VI , I' ] . .... It' is a setof linearly independent vectors from # ", then ( TIVI ) , TIVE) . .... TIVE'!' is a set of linearlyindependent 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 .