What does the property of linearity mean?

Question

Linear algebra

What does the property of linearity mean? and you can give an example.
For example, the internal law of composition, over the space
a + b = b + a (a, b - vectors) Is this a property of linearity?

Answer 1

The property of linearity in relation to space means that the addition of any two elements of this space or the multiplication of an element by a real number will give us an element of the same space.
For example, on the number line, the addition of two numbers will again lie on the number line, and so will multiplication by a real number.