00:01
In this question, we are asked to find the standard matrix of the transformation, which first keeps e1 unchanged and moves e2 to e2 plus 20 e1, and then reflects through the line x2 equals to negative x1.
00:17
So to get that standard matrix of the transformation, we need to know its action on the standard basis vectors, on our two standard basis vectors.
00:30
E1 equals to 1 0 and e2 equals to 01.
00:40
So we need to see what happens to the vectors e1 and e2 under the transformation.
00:46
And we are already given that information, right? so at least the first step.
00:51
So it says that e1 changes into e1 and e2 becomes e2 plus 20 e1.
01:00
So let's see, let's look at the picture.
01:09
Let's say this is the x1.
01:10
Axis and this is the x2 axis and we need the line x1 equals to negative x2 equals to negative x1.
01:20
That's basically is this line.
01:27
So let's draw e1 and at the first step the transformation t doesn't change e1 right? and at the second step it reflects e1 through x2 equals to negative x1.
01:43
In other words it reflects e1 through the blue line.
01:47
And if we do that, we are going to get this vector.
01:53
And that's going to be t of you 1.
01:57
And it seems like it has coordinates 0 and negative 1.
02:04
Now we need to do same for e2.
02:08
We need to create a picture for e2.
02:17
Same line, x2 equals to negative x1.
02:23
This is a vector e2...