A linear combination is a mathematical expression formed by multiplying a set of numbers, called coefficients, by corresponding variables or vectors and then adding the results together. For example, if you have two vectors, v1 and v2, a linear combination could look like a*v1 + b*v2, where a and b are scalars. Linear combinations are fundamental in various fields, including linear algebra and statistics. They help in understanding vector spaces, solving systems of equations, and performing operations like regression analysis. By combining different elements linearly, one can explore relationships and create new representations of data.