Hi there. Here is a short post of the concept of a linear combination found in Linear Algebra.
Suppose we have vectors in and scalars . The linear combination (and vector) can be expressed as:
where refers to the number of vectors (terms) and is the dimension of each vector. Each from i = 1, 2, … , r is of the form
A simple linear combination in is 6 . This would be equal to
An example of a linear combination in would be . This is equal to
The examples above are nice examples since we can apply vector operations. Sometimes we may not have scalars that are numbers; we would be stuck with .
Elementary Linear Algebra (Tenth Edition) by Howard Anton
The featured image is from http://www.euclideanspace.com/maths/geometry/space/vector/vec2dBases.png.