Basis (linear algebra)

Ok kiddo, let's talk about something called basis in linear algebra.

Imagine you have a big bag of toys. These toys are all different shapes and sizes. Now, you want to choose three toys from this bag and use them to make every other toy in the bag. That's what basis is all about - choosing a few things to make everything else.

In math, we use basis to describe how different things can be made by combining a set of other things. Let's use colors as an example. Suppose we have three colors: red, green, and blue. We can make any other color by combining these three colors in different ways. For example, we can make purple by mixing red and blue together or we can make yellow by mixing red and green.

These three colors: red, green, and blue are what we call basis vectors in linear algebra. We use them to create any other color we want. Just like how we can use the three toys we chose from the bag to create any other toy.

In linear algebra, basis is a set of linearly independent vectors that span a vector space. A vector space is a collection of vectors that follow certain rules. For example, all the colors we can create by combining the basis vectors have to be inside the vector space of colors.

So, basis is a way of selecting a few important things in a set that we can use to create everything else. In linear algebra, we use basis to create any other vector in a space by adding and scaling the basis vectors. Just like how we can make any other color by combining the three colors red, green, and blue.