00:01
In this question we have been given an inner product on r2 on the basis vector and it is given as e1 comma e2.
00:10
So e1 e2 are the elements of the basis vector for r2.
00:13
And the inner product of them is given as follows.
00:16
E1 e2 is same as e2 e1 inner product and this is given to be 3.
00:23
And then we have e1, e2, e2, e2 in a product which is equals to 9.
00:29
And this is e1 and e1 here.
00:32
So this is the information that we are having.
00:35
In the first part, we need to find the matrix representation of this inner product.
00:42
So what we are going to get? so matrix, let's say it is denoted by a, so it will be given by inner product of e1, e2, inner product of e1, and here i will get e2, e2, and here it will be e2, e2.
00:58
Okay, here it is e1 and e1.
01:01
So all these values we know, so it comes out to be 4, 3, 3 and 9.
01:07
So this is the required matrix representation.
01:10
Then in the next part, we have been given if vector v is equals to 4 minus 1 transpose, that it is a column matrix.
01:20
And w is given to be 2 times 1 transpose.
01:24
What we need to find, we need to find the inner product of vw.
01:27
So inner product of vw is given by v transpose, okay, so this is given by v transpose or let me write v only...