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- Jan 29, 2012

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I quote an unsolved question from MHF posted by user

P.S. Of course, I meant in the title

**jackGee**on February 3rd, 2013.[Let T:V->W Be A Linear Transformation

Where V and W are vector spaces over a Field F

let a={v_{1},v_{2},...,v_{n}} be a basis for V and b={w_{1},w_{2},....,w_{m}} be a basis for W

a) Prove that T is surjective if and only if the columns of [T]_{ba}span F^{n }

b) Prove that T is injective if and only if the columns of [T]_{ba}are linearly independent in F^{n}

P.S. Of course, I meant in the title

*and*instead of*an.*
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