Hello, could anyone help me with this excersise of linear algebra, Please?

Question

Well it's about linear transformation defined as T:V--W , the excersices give me a set of linearly independent vectors of V {v1,v2, v3... vk} and then asks :
Are {W1, w2, w3, ...wk}, the linear transformation of v1, v2,.. , also linearly independent?
How can I demonstrate that?

Answer 1

google the topic. You will find many good discussions, such as this one:

http://math.stackexchange.com/questions/584132/proof-of-linear-independence-of-vectors-after-applying-a-linear-transformation