CHAPTER 02.03: VECTORS: When are two vectors equal?

 

In this segment we will talk about when are two vectors equal. So two vectors, and letís suppose somebody says hey you have two vectors A and B when will they be considered to be equal, are equal if they are of the same dimension they are of the same dimension thatís the first requirement and the second one is that and the corresponding elements are same so what that means is that letís suppose somebody gives you column vector A and says hey I got column vector A with a1, a2, all the way up to a sub n-1, a sub n, I got n-entries in the A vector and I got another vector called B and it has b1, b2, all the way up to b sub n-1, b sub n, so I got n-entries in B so now we do have same number of entries in A and same entries in B but in order for A to be equal to B if the A vector is same as the B vector then what do you need to have we have a-i equal to b sub i for all values of i going from 1, 2, all the way up to n so it means that a1 has to be equal to b1, a2 has to be equal b2, a3 is equal to b3 for all the values of i which is from 1 to n only then will we consider two vectors equal. And thatís the end of this segment.