Prove That If T Rn &Gt

Rm is a one-to-one linear24. Prove that if’ T . {quot; – #` is a one – to- one linear transformation and S’ = (VI , I’ ] . …. It’ is a set
of linearly independent vectors from # quot;, 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 ) + [ ] ( quot; ; ) + … + CT ( VA ) = 1`
Rewrite the left side using the linearity properties of’ I’ and use the Kernel Test for Injectivity .Math