Two students are arguing about a certain question. The question states, \"Suppos

Question

Two students are arguing about a certain question. The question states, "Suppose that three vectors u, v, and w are such that w is not a linear combination of u and v. Is the set {u, v, w} linearly independent?" The first student argues that they must be linearly independent, because in class there was a theorem relating one vector not being a linear combination of the others to the set being linearly independent. The second student argues that they have come up with an example u, v, and w that fit the criteria but are linearly dependent. Who is correct?

Explanation / Answer

The first may not be right because he just cannot express W in term of U and V .It doesn't imply linear independence.

The second student could have expressed U in terms of V and W or V in terms of U and W ,so which implies linear dependence.

So set is linearly dependent and student 2 is correct if his claim is right.

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