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A vector is an ordered group of numbers. It has some integer size n, that is to say it has n numbers in it. Often it is writen with the arrow brackets like so v=<v1, v2, v3 ... , vn>

Because vectors are ordered <2,1> is different from <1,2>. An easy way to see this is to think that you are grocery shopping and the vector tells you how much apples you have as it's first component v1 and telling how much Oranges you have in the v2 component. It is clear that 2 apples and 1 orange is different from 1 apple and 2 oranges.

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