Determine whether the vectors V1 1 1 2 V2 1 0 1 and V3 2

Determine whether the vectors V_1 = (1, 1, 2), V_2 = (1, 0, 1) and V_3 = (2, 1, 3) span the vector space R^3.

Solution

DImension of R3 is 3 so if 3 vectors are to span R3 then they must be linearly indendent

But note that

v1+v2=(2,1,3)=v3

Hence, v1,v2,v3 are linearly dependent

HEnce do not span R3