What is a basis in linear algebra?

Problem Statement

What is a basis in linear algebra?

Step-by-Step Explanation

A basis is a set of independent vectors that spans a vector space.

1. Identify what the question is asking. In Linear Algebra, this usually means naming the known quantities, the unknown quantity, and the concept that connects them.
2. Write the relevant definition, rule, or relationship before substituting numbers or manipulating symbols.
3. Work one step at a time and keep units, signs, and restrictions visible.
4. Check whether the answer makes sense in the original context.

Final Answer

A basis is a set of independent vectors that spans a vector space. The reliable strategy is to start from the definition, apply the correct rule carefully, and then interpret the result in plain language.