Linear combination

Okay kiddo, imagine you have two toys: a toy car and a toy truck. Let's say you want to play with both toys at the same time. You can do this by combining them in different ways. For example, you can place the car on top of the truck or you can put the truck on top of the car. These are called different combinations.

Similarly, in math, you can have two numbers, let's call them "a" and "b". And just like with toys, you can combine them in different ways. For example, you can add them together: a+b. Or you can subtract them: a-b. These operations are called linear combinations.

But why is it called "linear"? It's because the operations you can perform (like adding or subtracting) only involve multiplying the numbers by a constant (a number that doesn't change) and adding or subtracting them. The word "linear" is used because when you graph these operations, they make a straight line on a graph.

So just like you can play with your toy car and truck in different ways, mathematicians can use linear combinations to explore different ways of combining numbers. And that's basically what linear combinations are, kiddo!