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## Homework Statement

Suppose that S = {v1, v2, v3} is linearly

independent and

w1 = v2

w2 = v1 + v3

and

w3 = v1 + v2 + v3

Determine whether the set T = {w1,w2,w3} is

linearly independent or linearly dependent.

## Homework Equations

Let c1, c2, c3=scalars

c1w1+c2w2+c3w3=0

c1v2+c2v1+c2v3+c3v1+c3v2+c3v3=0

(c2+c3)v1+(c1+c3)v2+(c2+c3)v3=0

c2+c3=0

c1+c3=0

c2+c3=0

solving 1st equation gives: c2=-c3

Plug into 3rd gives: -c3+c3=0 → 0=0 what does this mean?