### Example

If the variables *x* and *y* belong to a set of real numbers and *a* and *b* are integers, then the expression

\(z = ax + by\)

represents the real number *z* in the form of *a* linear combination of the integers *a* and *b*.

### Educational Note

The concept of a linear combination refers to two sets V and S of mathematical objects, which are vectors in a vector space and numbers or scalars in a numerical space, such as the set of real numbers. We define an external operation so that every element of V can be expressed as a sum of the products of a scalar of S and a vector of V. The number of terms in this product depends on the dimension of the chosen vector space. If the vector space is 2-dimensional, then each linear combination will include 2 terms; if the vector space is 3-dimensional, then each linear combination will include 3 terms; and so on.