00:01
Whatever you're going to find the elementary metrics.
00:04
Our first task, you're still fine.
00:09
Any american markets.
00:12
Mhm.
00:16
For a given metrics that is we got too close to metrics with 3121 is the numbers.
00:24
Okay, let us as you let the one are you doing or something like it? to the elementary matrix.
00:50
Yeah, sunday.
00:53
Yeah, you could.
00:56
Mhm.
00:57
You came in this one you don't um into the given metrics is the cost of the identity matrix where i is the identity matrix of a too close to.
01:11
There is 1001.
01:21
Do what you can see that play metrics as it goes to the inverse of all these elementary ck's.
01:29
That is you on the news and you're doing worse.
01:34
A group get it was now all we have to do is find these you want to do and you gain worse.
01:51
So we'll start by taking an identity matters on one side that is from 001.
01:57
And we have to multiply and do the operations on this subject.
02:03
We'll get our heart tricks which is given to us so you want to work.
02:08
So the start was start one x 1 the first we can do this we can do you one minus rodeo what i'm targeting right now that i have to make it as the elementary matters of something of this kind.
02:22
Something around the sort of this this is my budget to do that.
02:33
Yeah.
02:34
Once i do this operation.
02:36
Are you good? yeah minus one zero.
02:42
What? mm.
02:44
And this earlier the really useful that is 10.
02:49
The level of whatever i'm getting on this side.
02:55
This can be different as my first element hypnotics.
02:59
I'll take the and what's on the after all the remains are known but on the side we can keep it at this hour even now just to go again.
03:10
What i'll do i'll just copy the same thing so that the space transfer will not irritate us.
03:17
One minus 10 and one.
03:21
Good good.
03:23
Uh huh.
03:25
201 this is what we got on the last place.
03:28
I'm going through the second operation a little bit ar- who are one on this.
03:36
So we'll see what we go after doing this operation on both the sides.
03:41
I'll do it zero minus 21 and the same.
03:49
Even previous metrics.
03:51
And okay.
03:53
Doing the same thing on the right hand.
03:54
Seven is good.
03:55
One little 01 so that you currently mattered the self and this thing i can name it is my idea metrics now both even into even if you do is ready with me, what i can write is you do do you want into the matrix? is a cultural identity matrix.
04:18
Hence like we have seen in the previous page also is equals two universe.
04:23
Thank you.
04:25
You're doing most.
04:27
No.
04:27
The next question is how do we find the and also this? how to find a divorce? both a square matrix of cross too.
04:39
So let us as human square matters city with the elements a.
04:44
B.
04:44
Serie and i lose you that the determinant of the that is equals to 80 minus bc.
04:54
This into this is non zero.
04:59
Hence the piano's exist.
05:01
So the team was will be for a to cross two matrices with determinant that is a t minus bc.
05:09
And the remaining metrics.
05:10
I can just change it like this.
05:13
D a -7.
05:15
With a negative sign under -c.
05:17
This will be the painless.
05:19
So i'll do the same operation for e.
05:22
Even and you do like we have seen even was equals two 0 -101.
05:32
So by using the formula that we've written on the previous face even in worse will be equal to 1101.
05:45
You do was equals two 1 -20 and one.
05:51
If i do the inverse of this we're using that same form that i have right written down on the previous speech.
05:57
Okay one.
06:01
What's he doing now? so now i have my even metrics as well as my data matrix.
06:08
So hence i have both the metrics even and that is what we were targeting now the second part this includes the you have to reduce it into roy clinton.
06:26
That is already yes.
06:29
To start this part i start with the same metrics metrics that was equals two 321 and one.
06:39
One word one.
06:40
We have to do rule operations until and unless we reduce it to them.
06:44
Identity matrix form.
06:46
1st.
06:46
I do operation on the first road.
06:49
You multiply.
06:50
The first proof is one x 3.
06:55
Okay, 1, 1 x three.
07:00
Two and one.
07:02
No cooperation on the second row.
07:04
My target is to make this one is zero.
07:06
So what i'll do is our two minus two and 2 hours.
07:14
Yeah, i'll get 10 one battery one.
07:23
But so now the next target is i have my one i have my zero.
07:30
I have to make this one has one and this should be zero.
07:35
So to do those operations, what are you? are you on this? so and are multiplied this with three.
07:42
So what i did 1, 1 x three we learned to 30.
07:48
One battery into three will be one.
07:50
One of the work is over now.
07:52
The next target is to make the sun as one.
07:56
Sorry i have to make it at zero.
07:57
So what i'll do is ar minus.
08:01
Are you wetting? and so good.
08:07
1 001.
08:09
This is our identity matrix.
08:11
So it has been reduced in the royal pure in form.
08:15
Now the second part of the question states it is a long question and the second part asked me to do the value decomposition for a jury composition.
08:30
I have to do it on the same metrics.
08:32
The metrics was three on what? okay, we'll start with this.
08:38
Let me just define what if any do you first a loser a little.
08:46
Only the lower triangular matrix.
08:52
Similarly you is upper triangular matrix subject.
09:04
The matrix a can be written as product of the lower triangular matrix into the upper triangular matters.
09:09
And this is what we want to find it and you.
09:12
So i'll start with first i'll try to make it a particular metrics for a particular matters.
09:18
I will take our given matics and to make it up.
09:22
Triangle matters.
09:23
I'll do operation on the 2nd row.
09:27
Hello roto minus just to make it at zero...