00:01
Hi, so we can write it as the, maybe the coefficient matrix that is given as 1 to 3.
00:08
So we can write it as 1 to 3.
00:12
The coefficient matrix and then it is 345, 3, 4, 5 here.
00:19
And next is 5, 6, 1.
00:21
So we have 5, 6 1, right? just we write along with the constant matrix.
00:27
That is 246 here.
00:30
So we have 246, 5.
00:33
So what our plan is basically in the gaussian elimination method is the gaussian elimination.
00:42
So what we do in this method, that is the gaussian elimination, right? what we do basically is make here this matrix as the unit matrix, right? you make this matrix as the unit matrix, right? and then from here we get x1 x2 xxp.
00:59
Let's try to make this as a unit matrix by applying the row operations here.
01:02
So the first row operation will have basically so we apply here r2 tends to you want to bring this out as zero basically we make it as zero so we'll get r2 minus 3 r1 so we get right and simultaneously we can make this as zero we apply r3 tends to r3 minus 5 r1 right it will become zero you can see that so you just get the matrix now the first row will be at this one through three and this will be two next we have r2 minus three hour one so we get three minus three times one that'll give you zero next four minus three times two right that is giving you minus two next we have five minus three times three that is giving uh minus four right and then we have four minus three times two that is giving minus two here right and next year we have our three tends to r3 minus 5 for 1 this will give 0 here then 6 minus 5 times 2 that's giving minus 4 and then 1 minus 5 times 3 that is giving minus 14 and then we have 6 minus 5 times 2 so that is giving minus 4 right this we get here so uh this we get now uh just going to have to be here 0 here and this we get 0 here and this we got 0.
02:40
Next purpose is we need to make this as zero here and this as zero, right? what you can do now? see, here we have two, right? and here we are minus two.
02:53
So here we have two, here we are minus two.
02:55
We just add them.
02:56
We'll add this as zero basically, right? and then we have here minus four and here we have minus two.
03:06
So apply the operations here to make it as zero.
03:09
So let's go for that.
03:10
Or one more thing, what we can do here.
03:12
We have here minus 2 minus 4 so we can make this as 1 right so as applied here we'll have r2 tends to r2 divide by minus 2 right this we get apply that so the row 1 as it is you get 1 2 3 and this will give 2 here then r2 or minus 2 is 0 only then minus 2 or minus 2 is giving 1 and minus 4 over minus 2 that is giving 2 and minus 2 or minus 2 that is giving 1 right this we get 1 here and after 3 as it is 0 minus 4 minus 14 and here we are minus 4 the next part is okay now we can look in this way the next part is so this part we're to make it as 0 you make it as a unit matrix see let me show you the 3 cross -3 unit matrix it is given like that 1 -0 010 and then 0 0 0 0 0 0 0 and then 0 0 0.
04:13
That is 3 cross 3 unit matrix.
04:16
That means we want this matrix here, the coefficient matrix to be in this form, right? that's why we're applying here the row operations.
04:24
Next one is we can make this as 0, we can make this as 0.
04:27
See how? apply here, r1 102 will have r1 minus 2r2.
04:34
It will make this as 0, right? let's apply r3 102, r3 plus 4r2, right? will make this as 0.
04:44
Let's apply that.
04:46
So we get here, r1 will be, this is going to be 0.
04:52
Next we have 3 minus 2 into 2.
04:56
That is giving minus 1, right? and it will be 2 minus 2 times 1, that is giving us 0.
05:04
So you get it as 0.
05:07
The next r2 as it is 0, 1 2 and here we have 1, right? and r3 is given as r3 plus 4r2.
05:15
So this is come out of 2.
05:16
To be 0 only.
05:18
It will give 0 minus 4 plus 4 that is giving 0 then minus 14 plus 8...