Prove that if spanv1 v2 v3 V then v V v v1 v2 v3 is linea

Solution

Given that {v1, v2,v3} vectors span V

This implies

i) v1,v2,v3 are linearly independent

ii) Any vector in V can be represented as a linear combination of v1, v2, v3.

So for any vector v in V

v = av1+bv2 +cv3

This implies that {v1,v2,v3,v} are linearly dependent since v can be represented as a linear combination of other 3.