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00:00Look, there are 3 columns and 3 columns, 1, 2, 3, 4, 5, 6, 7, 8, 9.
00:06Open it, remove it, remove it and see what it is coming.
00:10Just tell me, it will be 0 and what will it be? Singular mattress.
00:15It will be 0 and I want to tell you a special question.
00:20Look, when the mattress will be perfect 0?
00:27How many numbers are these?
00:281, 2, 3, 4, 5, 6, 7, 8, 9.
00:31That means, if you have a perfect square, keep it, it will be 0.
00:38Like if you look at this, it will open 5 to 5 and it will be a big number.
00:42Aqsa logo, it will show you the band.
00:44But since I know the tricks of my students, there is no problem.
00:481, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 24.
00:58If you look at this, it will be 25 to 25, what will be 0?
01:02If you look at this, what do we call it? Singular.
01:05Then my brother, a very little bit of information.
01:07Let's just pretend.
01:08If you are a result and a result of the error,
01:10let's start.
01:11So, it's like 1, 2, 3, 4, 5, 6, 7, 9, 10, 15, 16,
01:15just not determine zero.
01:17Listen to this one other way.
01:19When you look at a result of the error,
01:21what is the benefit of this error?
01:23In this case, he said he gave a lambda.
01:26He said he did not lose the determinant.
01:29Sorry not, not the determinant.
01:30But he said that
01:31the matrix is singular
01:32and it will lose the value.
01:33What are you doing?
01:34and put it equal to 0
01:36and put lambda value
01:38but if we know the trick
01:40we will think
01:421, 2, 3
01:44here is a miss
01:46then 5, 6, 7, 8, 9
01:48then let's see here
01:504 is a miss
01:52let's give this 25
01:54i.e. 5 row 5 column
01:56here too
01:58let's miss this
02:00or give x
02:02determinant is singular
02:04equal to 0
02:06we will solve 5 row 5 column
02:08no
02:101, 2, 3, 4, 5
02:12what time is 7?
02:14the answer will come
02:16now we have to ask a question
02:18in the matrix determinant
02:20what we have to ask
02:22is that we have to ask
02:24one topic
02:26physics or chemistry
02:28and when this course is completed
02:301, 2, 3, 4
02:321, 2, 3, 4
02:341, 2, 3
02:36and every year
02:38so
02:40this is the target of 100 marks
02:42so
02:44the answer here is 7
02:465 rows 5 columns
02:485 rows 5 columns
02:50you do not have to see
02:52see the matrix
02:54and you have to see the earth
02:56and you have to see the earth
02:58and see the earth
02:59this is the diagonal
03:00matrix
03:02because all members are 0
03:04so diagonal
03:05or lower upper triangle matrix
03:06its determinant
03:08its number
03:10multiply
03:112-3-6
03:136-2-12
03:1412-1-12
03:1512-2-24
03:16Now in past 7
03:17I was coming
03:18to see the band was changed
03:19and I was saying
03:20this was what I had
03:212-3-6
03:226-2-12
03:2312-12
03:2412-12
03:2512-24
03:26and this is now the answer
03:27Yes, the nurses are very big
03:29They are seeing this
03:30the proof
03:31I was doing that
03:32What a question
03:33x plus 1
03:35x plus 2
03:36x plus 3
03:37x plus 4
03:38x plus 6
03:39x plus 7
03:40x plus 8
03:41x plus 9
03:42and this is the determinant
03:43How do we make it?
03:45Open multiply
03:46x
03:47and solve
03:48x
03:49My children
03:50When it happens
03:51when it happens
03:52one of my heroes
03:53I take the help of my heroes
03:55My hero's name is 0
03:58If there is 0
03:59then there is a side hero
04:01where we use 0
04:02We use 1
04:04x to 0
04:05Well, like I have 0
04:07this year
04:08this year
04:09there is 15-16
04:10times
04:11this year
04:12What is this?
04:14What is this?
04:15Now
04:161-2-3-4-6-7-8-9
04:18has come up
04:19Now
04:20I said
04:211-9
04:22in the order
04:231-9
04:241-2-4-9
04:251-9
04:261-9
04:271-9
04:281-9
04:291-9
04:301-9
04:31closing
04:332-7
04:34pop
04:351-9
04:37Gang
04:391-9
04:412-9
04:441-9
04:451-9
04:461-9
04:471-9
04:483-9
04:491-9
04:491-9
04:501-9
04:511-9
04:521-9
04:521-9
04:531-9
04:541-9
04:551-9
04:562-9
04:571
04:581-9
04:582-2
04:59So, now I have a very awesome trick.
05:11Awesome!
05:12Look, if there are 3 things in raw, in every raw,
05:151, omega, omega, square.
05:17Is there not?
05:18Omega, omega, square, 1.
05:20All things are at once.
05:21Absolutely.
05:22Okay, either raw or in the column.
05:25It's not necessary in both.
05:26Here, the raw or in the column is running like this.
05:29Look, it's all over.
05:30One, omega, omega, square.
05:323 things are also coming in raw and in the column.
05:35Here, the raw is not coming in raw.
05:37It's not necessary in both.
05:40And here, when there is multiplication,
05:43it also is 3 things.
05:44Whenever it happens, what is the answer?
05:460 and 9.
05:50This is a good trick.
05:53Isn't it?
05:54If a square is equal to one,
05:56It's important.
05:57It is important.
05:58Yes.
05:59it's important.
06:00If a square and a square come in to zero,
06:03it's not important.
06:05If a square is equal to one,
06:07it'll be equal to one.
06:09It's symmetric.
06:10Then it will be important.
06:14I suppose if it is minus A, then it is symmetric.
06:17If you have a small matrix and it will be identical to the identity matrix.
06:23If it is 2 rows and 2 columns, then it will be 2.
06:26If it is 3 rows and 3 columns, then it will be 3.
06:29This will be done.
06:34If I is equal to I, then I transpose A, then it will be symmetric.
06:42The matrix A transpose is minus, but I will not skip the matrix.
06:45It is like this.
06:47I will give two questions first.
06:50One omega omega square, then omega omega square one, then omega square one,
06:55omega square one, omega square one, omega square one, omega, omega square one,
07:01omega square one, omega square one, omega square one.
07:04It will be equal to this scale.
07:06We will plus these two matrices.
07:09Now I will tell you a big trick.
07:14Look.
07:15In this row, there are 3 rows of 1 omega and omega square three.
07:19Is it like this?
07:201 omega and omega square three?
07:23Yes.
07:24Is it like this?
07:25Yes.
07:26Is it like this?
07:27Yes.
07:28It is like this.
07:29It is like this.
07:30It is like this.
07:31Only 3 row number one mpo is one omega and omega square.
07:36Let's see.
07:37Let's read the diagram of it.
07:38It's like this.
07:39It is like this.
07:40Let's look at it.
07:41It can make a difference.
07:42Each row stays in row.
07:43Top of each row is like this.
07:44The rows are in this row.
07:45Which be Çamakar has蛇 and so in column it is like this.
07:47It is actually like the table.
07:48Once there exists, The result of thiseterretenation will turn natural.
07:50The result is 0,0.
07:54The result of A is equal to D of S.
07:58If A is equal to D of S,
08:00then the matrix B is equal to transpose of A,
08:04then B is equal to D of D.
08:06The transpose means that
08:08is to draw a column and draw a column.
08:10If draw a column and draw a column,
08:14there is no determinant.
08:16Therefore, if A is equal to D,
08:18if A is equal to 12,
08:20then B is equal to D,
08:22it will be equal to 12.
08:24So, it will be very good.
08:26Now, one question is,
08:28A dot B is equal to 0.
08:30Well, A dot B is equal to theta 90,
08:32or theta 270.
08:34Now, 90 is equal to pi by 2.
08:38270 is equal to 3 by 2.
08:40If you remember,
08:42the answer is equal to pi.
08:44So, A dot B is equal to 0.
08:46So, this is 0, theta 0,
08:48180, and 360.
08:50Well, 180 can we have to do it,
08:53and 360 can we have to do it.
08:55Now, some other great fun of it.
08:59One time,
09:01the answer is,
09:02that A dot B is equal to 0.
09:04So, that A dot B does not equal to 0.
09:08Which one is equal to 0?
09:09So, we will have that trick.
09:11We will say,
09:12theta does not equal to 90,
09:13or theta does not equal to 270.
09:15Theta does not equal to pi by 2,
09:17theta does not equal to 3 by by 2.
09:19This is how,
09:20A cross B does not equal to 0.
09:22When theta does not equal to 0,
09:24does not equal to 180,
09:25does not equal to 360.
09:26180 to pi,
09:27360 to 2 pi,
09:29But if you have a simple concept, if you have a determinant of 1 or minus 1, then the matrix is more than a normal matrix.
09:42In this case, the matrix is equal to a transpose.
09:47Now, the matrix is 0, 1, 0 and 0, 0, 0, 0, 0.
09:52And you say, this is inverse.
09:54So, first of all, you have a determinant.
09:56What will it be?
09:58Or minus will it be?
10:001 and minus 1 will come.
10:02So, you don't have a determinant.
10:04So, you don't have an inverse.
10:06You don't have an inverse.
10:08So, you don't have an inverse.
10:10You don't have a transpose.
10:12You don't have a column.
10:14Now, first of all, the row is 0, 1, 0.
10:16You don't have a column.
10:18The other row.
10:20So, if you don't have a matrix, you don't have a matrix.
10:22It's a box.
10:24Is it transpose and a matrix?
10:26Yes.
10:27And the matrix and the transpose A, what can be given to the matrix?
10:32Symmatris.
10:34Symmatris.
10:36So, you can say that.
10:38That's your answer.
10:40That's your answer.
10:42It's a big deal.
10:44Now, you have a big deal.
10:46You have a determinant of the minus 1.
10:48And you have to say that this is the determinant of the matrix.
10:52Now, let's take a look.
10:54Here, the row is 130.
10:56Here, the row is 260.
10:57Here, the number is double up.
10:58See, the first row we have to multiply.
11:00Which row?
11:01Which row?
11:02Which row?
11:03Which row?
11:04Which row?
11:05Which row?
11:07Which row?
11:08Which row?
11:09Which row?
11:10Which row?
11:11Which row?
11:12Which row?
11:13Which row?
11:14Which row?
11:16Which row?
11:17Which row?
11:18Minus 12.
11:19Two 2 is up.
11:20Two is up.
11:21Eight.
11:22Minus 12.
11:23Minus 13.
11:24These are the answers.
11:25Do you do that?
11:26We will find the questions very well?
11:27How do we do that?
11:28Second answered.
11:29Does the second answer do that?
11:31Its 2.
11:32Okay, boys, one thing is that the question that I have given was the answer to this one, which is minus 2, okay?
11:39Now, in this one, we do this.
11:43Like that, the determinant is missing, so this one will tell us that it is 4.
11:47Now, how will the checking?
11:49We will keep the x to 0, which is 4.
11:52So, all these options will come from b.
11:55Look, the x is vectorial, i.e. 0 is vectorial 1.
11:58Here is 2.
12:001 vectorial 1, 2 vectorial 2.
12:02How much is it? 4.
12:04So, this answer will come from b.
12:06Again, people.
12:07The x is vectorial 0, vectorial 1.
12:09This is 2.
12:10It will cancel out.
12:11Is it 0 or 2?
12:13It will cancel out.
12:14This is 1 vectorial.
12:16And this is 2 vectorial.
12:182 vectorial is also 2.
12:192 vectorial is 4.
12:20Let's see from any other options.
12:21It is not 4.
12:23This is 3 vectorial 6.
12:25This is 3 vectorial 6.
12:262 vector is 12.
12:27And this is not 2.
12:29It will cancel out.
12:30So, the correct answer will be your option.
12:32It will be better entering when the question comes from algebraic.
12:36So, our hero is 0.
12:39Here we have x to 0.
12:40Here we have x to 0.
12:41Here we have x to 0.
12:42Here we have x to 0.
12:43Here we have x to 0.
12:44Here we have x to 0.
12:46Now, the x to 0.
12:48Here we have x to 0.
12:49This is a very simple question.
12:50I will say that these diagonals are just multiply them.
12:553, 4, 12, 12, 12, 5, 60.
12:58This should be answered.
12:59Here we have x to 0.
13:024, 4, 16, 16, 4, 64.
13:05But kids, take it and take it.
13:07First, this is like this.
13:09Now look at diagonal.
13:11The bottom of the diagonal is zero.
13:13The upper one is not zero.
13:15Now how will you put the determinant?
13:17The determinant will also be like this.
13:19They will multiply this.
13:213, 4, 0, 12, 5, 0, 16.
13:23But, but, but, but, but,
13:25what are the main things?
13:27What are the main things?
13:29It is called lower triangle.
13:31Who are the main things?
13:33Diagonal is zero.
13:35Diagonal is upper member is zero.
13:37This is called lower triangle.
13:39So, what is the last thing?
13:41This is the determinant.
13:43But, now I will give it to you.
13:45Determinant will also be like this.
13:48Or 64.
13:50But, if the upper part triangle is zero,
13:52it is called upper triangle.
13:54Now, we have studied A, B, C, D.
13:56Some say that it is adjoint.
13:59Adjoint matrix is how it is?
14:02How is the part of A and D?
14:04given the importance of B, C and B.
14:08What will be given to you?
14:09Minus will be given to you.
14:11Very important.
14:13The more important part,
14:14The more and the plus were given to you,
14:16In the other part, minus will be given to you.
14:19I mean, A and D will be given to you.
14:20They are given to you,
14:21and both will turn to you.
14:22And, what will happen to A inverse work?
14:24Adjoint, A code, Divide, A Determinants
14:28But, A Determinants, which is AD-B, is 0
14:33And if this is 0, then the mattress will play, Singular Mattress
14:37What will it play? Singular Mattress
14:39We are going to trick it
14:41We are going to see the questions
14:43We are going to solve the problems
14:45We are going to explain the basic concepts for people
14:49We are going to take the basic concepts
14:51Now I am going to start thinking of
14:53Don't worry
14:54Let me tell you
14:56There are many advantages of the video
14:58The integration of the glass
15:00I am going to make the minimum 50, 60%
15:03Now I am going to see every 100 or 200
15:06I am reviewing for more各-40 questions
15:09I will think about how will I be practicing
15:12I will just look at to learn
15:14Ok dear
15:16So we are going to try to come to the mattress
15:181, 2, 3, 4
15:201,4 is 4, 2,3 is 6, minus 2.
15:27Now, the sign of both of them is 4 and 1, minus 2, minus 3, and this is minus 2.
15:38Now, let's divide from minus 2 and divide from minus 2.
15:49This will be the answer.
15:52Now, the chapter of the mattress is starting.
15:55So, let's see.
15:57This is a rock.
15:59How many rocks are these?
16:022 rocks.
16:03And what are these columns?
16:05How many columns are these?
16:073.
16:082 rocks, 3 columns are a big non-insaf.
16:11And who is the non-insaf in the mattress,
16:13the mattress is not a square mattress,
16:16but it is a rectangle mattress.
16:18How many rocks are these?
16:201 and 1 and 2.
16:21How many columns are these?
16:232 columns.
16:24It is completely clear.
16:25So, this is the square mattress.
16:27The square mattress is also coming out.
16:30A, B, C, D.
16:32Multiply.
16:33AD minus BC.
16:34It is coming out.
16:36It is not so difficult.
16:38Now, let's see this mattress.
16:40There is only one column.
16:42This is the column mattress.
16:44Look at this mattress.
16:45It is only a row.
16:46This is the row mattress.
16:47What will happen?
16:49It is only diagonal members.
16:52The rest are zero.
16:54It is only diagonal members.
16:56The rest are zero.
16:57Diagonal mattress.
16:59This is the same.
17:00This is the same.
17:01Diagonal mattress.
17:02The rest are zero.
17:03This is the same.
17:04Diagonal mattress.
17:05But, but, but, but, but.
17:07The same.
17:08The same.
17:09The same.
17:10The same.
17:11Which member?
17:12The same.
17:13The same.
17:14The same.
17:15The same.
17:16The same.
17:17The second.
17:18The same.
17:19The same.
17:20This.
17:21The next.
17:22The same.
17:23The same.
17:24The outer column mattress.
17:25Are properties.
17:26The same.
17:27And the same.
17:28Theisme.
17:29The same.
17:30The same.
17:31They are necessary.
17:32The other.
17:33Cover them.
17:34And the.
17:35A, a, b, c, and a.
17:37This is a very important basic concept of mattresses.
18:07This is a very important concept of mattresses.
18:09And the rule of mass is,
18:11if two rocks are the same as a determinant,
18:16if the second rock is the same,
18:18then the second rock is equal to zero.
18:20What is that?
18:21Zero.
18:22Zero.
18:24Now, people say that it is fundamental.
18:27Basic properties are the problem.
18:30And that is the approach.
18:32Now, this is a doubt.
18:34The problem is that it is a mattress that is the value of x.
18:39When the mattress is the same,
18:41its determinant is zero.
18:43Now, zero is so much in my opinion.
18:45When the mattress is zero,
18:47when the two rocks will be the same.
18:50This is not the same.
18:52It is not the same.
18:54If we multiply the two to minus two,
18:56then we multiply the four to minus two.
18:59Then we multiply the four to minus two.
19:01Then we multiply the four to minus two.
19:03Okay.
19:05Now, what is that,
19:06what if weimo and the one too.
19:08what if we multiply the four to minus two,
19:10it might be better than we multiply.
19:13You remember because we multiply the five just that.
19:15but if it is minus two to double,
19:16our need to I multiply the 14 so that we make a difference,
19:17therefore,
19:18The problem is not sucks.
19:19So, IKO,
19:20that people end correctly,
19:21mean,
19:22that the whole thing is versa.
19:23So,
19:24surely
19:26Well,
19:28situation is same.
19:29Now,
19:30If you look at the element of the element which means minus x, you can minus 4
19:35and this element of the element minus x is equal.
19:38If you look at this element, this element is minus 9 plus x is equal.
19:44If you look at the element of the element, the element is minus 2.
19:48That's the one for this element.
19:50It's very easy to say.
19:51You don't have to do x here, sir.
19:53We don't have to do x here anymore.
19:541
19:57Can you find a determinant if A matrix equal to
20:07This raw ABC, 0B, A
20:11What is common?
20:12This is diagonal ABC
20:14And diagonal under all 0 are
20:16Diagonal under all 0 are lower triangle
20:19Diagonal under all 0 are upper triangle
20:22And this answer is diagonal multiplication
20:25A multiply go B, B, C, A, B, C answer
20:28And if you see this in the second question
20:31It is written by the number 1, 2, 3, 4, 5, 6, 7, 8, 9
20:35If you write the number entirely by the number 1
20:38Then the determinant is 0
20:40Or if it is diagonal 0
20:43If it is diagonal 0, then the determinant is 0
20:46So here you hold it
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