# What Is A Linear Combination?

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

Examples

Example One

A simple linear combination in is 6 . This would be equal to

Example Two

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 .

Reference

Elementary Linear Algebra (Tenth Edition) by Howard Anton

The featured image is from http://www.euclideanspace.com/maths/geometry/space/vector/vec2dBases.png.