The first part of your proof correctly shows that **a** being a scalar multiple of **b** implies that such scalars exist, and so **a** and **b** are linearly dependant. The second part of your proof, I think, can be made more rigorous by saying that **a** is not a scalar multiple of **b** implies that there exists no *k* such that **a**=*k***b**, so the scalars required for linear dependance do not exist.

All in all though, I think your proof is valid.

]]>Prove that two vectors, **a** and **b** are linearly dependent if and only if **a** is a scalar multiple of **b**.

Proof:

If **a** = k**b**, then **a** - k**b** = 0, and the system is linearly dependent.

If, however, **a** ≠ k**b**, then **a** - k**b** ≠ 0, and the system is not linearly dependent.

My book gives the hint that we should consider separately the case where **a** = **0** (the zero vector), but that just seems superfluous and unnecessary to me.

What do you guys think?

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