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

1. Owlfred

Hoot! You just asked your first question! Hang tight while I find people to answer it for you. You can thank people who give you good answers by clicking the 'Good Answer' button on the right!

2. nedved365

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.