00:01
All right.
00:02
So in this question, we're asked to find the matrix representing the reflection over a line l and the line consists of the multiples of the vector 3, 5.
00:10
And just a recap of how these things are done.
00:13
So if we have a general line in here whose angle with the, whose angle with the x -axis is alpha, then the reflection over alpha is given by the matrix here, cosine of 2 -alpha, sine to alpha, sine to alpha -sign to alpha -minus cosine.
00:33
To alpha, right? so now we can do this as we'd like.
00:43
All right, so only thing we need to do really is to draw the line and calculate the angle it makes with the x -axis.
00:50
But of course, so in our case, our picture will be something of the form.
01:01
So our line goes through zero.
01:03
Of course, it's all the multiples of 3 -5, so in particular, in particular.
01:10
Zero is there.
01:11
So if we have, say, three in here, five in there...