CHAPTER 02.04: VECTORS: When are two vectors equal? Example
In this segment we will look at when are two vectors equal we’ll look at an example. So, let’s suppose somebody says “Hey if A-vector is given as 2, 7, 11, 13 let’s suppose and B is given as 2, b2, 11, b4” then when is A-vector equal to the B-vector. So for example, somebody’s giving you - asking you “Hey what will make A and B to be equal.”
The first thing we try to check is that, hey, are the dimensions the same. So we have four entries here in the column vector, we have four entries in the column vector here. Then what we are going to see is that each corresponding component is the same. That means that the first component here has to be the same as the first component here; second component here has to be the same as the second component here; third has to be here, and fourth also has to be the same. So we are already finding out that, hey, a1 is equal to b1 is equal to 2, two and two, then a2 is equal to 7 and that has to be equal to b2 only then it is possible for the two vectors to be equal then a3 is equal to b3 is 11 and the last one is a4 is equal to 13 is equal to b4 so we’re already finding out that a3 and b3 are the same.
So that test is ok; that check is ok, and a1 the same as b1. But we’re not given the value of b2, but if we want the two vectors to be equal we have to have a2 the same as b2. So the b2 has got to be 7 and the same thing here that we’re finding out that a4 is 13; b4 is not given but if we want the two vectors to be the same then a4 has to be equal to b4 so b4 has to be equal to 13 and b2 is equal 7. So what’s going to make it to be the same is if b2 is equal to 7 and b4 is equal to 13. And that’s what’s going to make the two vectors to be equal. And that is the end of this segment.