## LeoMessi Group Title How can the linear combination of two non singular and linearly independent vectors encompass the whole of 2D euclidean space? 3 years ago 3 years ago

You asked how so I am assuming the question isn't why you need specifically, 2 linearly independent vectors. Well consider the independent vectors v1 and v2 being (a,0) and (0,b) . I can get any vector (c,d) by multiplying v1 and v2 by some 2 scalar values and adding v1 and v2 together:$\alpha _{1}(a,0)+\alpha _{2}(0,b) = (\alpha _{1}a, \alpha _{2}b)=(c,d)$ The simplest case to consider is the elementary vectors above with a and b both equaling 1. Then you just need to specify two alpha values.