CHAPTER 02.19: VECTORS: Rank a set of vectors Example 2
In this example, we’ll look at what the rank of a set of vectors is. SO let’s suppose somebody says: given A1 vector equal to 25, 64, 89; then another vector is given as A2 is equal to 5, 8, and 13. And another vector is given as A3 is equal to 1, 1, 2. Find the rank of the set of vectors. So we are doing that – the first thing which we know is that the rank of the set of vectors is going to be less than or equal to three. Because the dimension of the vectors is three, so it has to be – it can only be less than or equal to three. Let’s see what the number is which is less than or equal to three. We already know from a previous example that A1, A2, and A3 are linearly dependent. So A1, A2, and A3 are not linearly independent: they are linearly dependent. So that means that your rank of a set of vectors, which is given to you, the three vectors which are given to you; they’re going to be less than or equal to 2, because it cannot be 3 - because you don’t have 3 vectors which are linearly independent. So how do we figure out –hey, is it 2, is it 1, is it 0? If you look at A1 and A2, let’s suppose, if I Take A1 and A2 they are linearly independent. You can show that. So you can show that A1 and A1 are linearly independent, then in that case the rank of set of vectors is going to be equal to 2. And that’s the end of this segment.