# Basis (linear algebra) facts for kids

In linear algebra, a **basis** is a set of vectors in a given vector space with certain properties:

- One can get any vector in the vector space by multiplying each of the basis vectors by different numbers, and then adding them up.
- If any vector is removed from the basis, the property above is no longer satisfied.

The dimension of a given vector space is the number of elements of the basis.

## Example

If is the vector space then:

is a basis of .

It's easy to see that for any element of it can be represented as a combination of the above basis. Let be any element of and let .

Since and are elements of then they can be written as and so on.

Then the combination equals the element .

This shows that the set is a basis of .

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Basis (linear algebra) Facts for Kids. *Kiddle Encyclopedia.*