Answer to Question #242703 in Linear Algebra for Stan Wang

Question

A^4 a^3 a^2 a I linear combination

Answer 1

In mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be an expression of the form ax + by, where a and b are constants). The concept of linear combinations is central to linear algebra and related fields of mathematics. Most of this article deals with linear combinations in the context of a vector space over a field, with some generalizations given at the end of the article.

Let V be a vector space over the field K. As usual, we call elements of V vectors and call elements of K scalars. If v₁,...,v_n are vectors and a₁,...,a_n are scalars, then the linear combination of those vectors with those scalars as coefficients is ${\displaystyle a_{1}\mathbf {v} _{1}+a_{2}\mathbf {v} _{2}+a_{3}\mathbf {v} _{3}+\cdots +a_{n}\mathbf {v} _{n}.}$