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Linear Independence of Vectors

Maryk1993

I have been given the vectors u+2v, v+3w and w+4u and need to show that these vectors are linearly independent. I know how to show that vectors are linearly dependent, but I'm not sure how to how that they are linearly independent. Thank you for any help :smile:

Reply 1

Noble.

I take it you've also been told

\{u,v,w \}

is a linearly independent set, otherwise the question isn't true?

Reply 2

Maryk1993

Oh yeah sorry, I forgot to write that part.

Reply 3

maths learner

Original post by Maryk1993

Oh yeah sorry, I forgot to write that part.

If the vectors are linearly independent then it means that the scalars are all equal to 0 when you take linear combinations. Can you see where to go from there?