This computer science video is one of a series on linear algebra for computer scientists. In this video you will learn about linear combinations of vectors, that is, you will learn how to create new vectors by scaling then adding other vectors together. You will also learn that some sets of vectors can form bases (plural of basis) for the creation of all other vectors within a particular vector space, through linear combination with the appropriate scalar coefficients. In particular, you will see how a pair of linearly independent two dimensional vectors can be used as a basis for the creation of all possible vectors in two dimensional space. The terms span, linear dependence, linear independence and zero vector are defined. You will also be introduced to the standard basis, namely a basis comprised of orthogonal unit vectors, sometimes referred to as an orthonormal basis.