1. Let V and W be finite dimensional vector spaces with dim(v) = dim(w). Let {v1,v2,...,vn} be a basis for V. If T:V->W is a one to one linear transformation, determine if {T(v1), T(v2), ... , T(vn)} is a basis for W.(adsbygoogle = window.adsbygoogle || []).push({});

2. How do i get a matrix out of this: Let A be an 8x5 matrix with columns a1, a2, a3, a4, a5, where a1, a3, and a5 form a linearly independent set and a2=2*a1+3*a5, and a4=a1-a3+2*a5.

I have looked all over, and I have starts to each of these problems, any help would be received with much thanks.

So far, for 1. I know that it is true by a theorem I found, but I am really unsure how to prove it.

on 2. I made a matrix like this

1 2 0 1 0

0 0 1 -1 0

0 3 0 2 1

I reduced it and came up with the answer that the dimension of NulA is 2 because it reduces to having 2 free variables.

If this is the wrong way to get the matrix A, how do I do it?

Thanks.

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# Linear algebra questions

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