What is a linear combination?

A linear combination is an expression formed by multiplying a set of vectors by corresponding scalar coefficients and then summing the results. Mathematically, if ( v_1, v_2, \ldots, v_n ) are vectors and ( a_1, a_2, \ldots, a_n ) are scalars, then the expression ( a_1v_1 + a_2v_2 + \ldots + a_nv_n ) is a linear combination of those vectors. Linear combinations are fundamental in linear algebra and are used to explore concepts like vector spaces and span.