Matrix 1-Part1

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Transcript
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00:04:48Dear students, Assalamu Alaikum.
00:04:50Welcome to today's lecture.
00:04:52Can you hear me clearly?
00:04:54Please let me know in the chat box.
00:05:01Walaikum Assalam.
00:05:05Can you hear me clearly?
00:05:07Please let me know in the chat box.
00:05:09Ok, all clear.
00:05:11Ok, so first I will give you my information.
00:05:13Today is your first class.
00:05:15So, let me introduce myself.
00:05:17My name is Abdul Rehman Karim.
00:05:26Nickname is knife.
00:05:30I am studying in the EEE department
00:05:32in Dhaka University.
00:05:34My school and college is Dhaka Residential and Model College.
00:05:36I am studying in the residential department
00:05:38from class 3.
00:05:42So, today we will start
00:05:44chapter 1.
00:05:46Our matrix.
00:05:48This is our first lecture.
00:05:50So, let's start.
00:05:52Ok, so see
00:05:54first I will give you an idea
00:05:56about matrix.
00:05:58What is matrix?
00:06:00Matrix is your organized data.
00:06:02You will have some data.
00:06:04If you organize those data
00:06:06in a nice way,
00:06:08then we call it matrix.
00:06:10For example,
00:06:12I have given an example of matrix.
00:06:14Mishuk, Jamil, Saurabh, Barunil, Fahim
00:06:16are given in Math, Physics,
00:06:18Chemistry and ICT.
00:06:20Now, I am taking all these
00:06:22data
00:06:24and writing it in a serial form.
00:06:26I have written all the marks.
00:06:28Now, I will ask you
00:06:30that if I want to write
00:06:32all these data in a nice format
00:06:34in matrix, then how will I write?
00:06:36That is with a series and column.
00:06:38You can tell me
00:06:40how many series do I have here?
00:06:42Series means
00:06:44your experience.
00:06:46How many experiences
00:06:48do you have here?
00:06:50One, here one series.
00:06:52Tell me how many series are there?
00:06:56Five, exactly.
00:06:58Tell me how many rows are there?
00:07:04How many rows are there?
00:07:06Five rows.
00:07:08How many columns?
00:07:10Four columns.
00:07:12How can I write
00:07:14any matrix?
00:07:16With a series and column.
00:07:18The definition of matrix is
00:07:20with a series and column.
00:07:22I have written a matrix here.
00:07:24I will write the expression here.
00:07:28Normally, matrix is written
00:07:30with third bracket.
00:07:32Maximum case is like this.
00:07:34In many places, first bracket is used.
00:07:36In some places,
00:07:38two bars are used.
00:07:40But, for me,
00:07:42most commonly used
00:07:44is this.
00:07:46Most commonly used
00:07:48is this.
00:07:50Third bracket.
00:07:52Now, this 5 by 4
00:07:54which is given here,
00:07:56what is this?
00:07:58This is called your chrome.
00:08:00This is called our chrome.
00:08:02What does chrome mean?
00:08:04Chrome means
00:08:06your
00:08:08series
00:08:12into
00:08:14columns.
00:08:16Series and columns.
00:08:18Now, I have
00:08:20many data here.
00:08:22For example, I have 99 data.
00:08:2496 data.
00:08:26Each of these data
00:08:28is our matrix.
00:08:34In English,
00:08:36it is our entry.
00:08:38Now, you tell me
00:08:40how many entries
00:08:42I have here?
00:08:44I am Bambhati.
00:08:50Tell me.
00:08:5220?
00:08:54Exactly, 20.
00:08:56Because you have 5 series
00:08:58and 4 columns.
00:09:00So, I will have 20 entries.
00:09:02So, from my matrix,
00:09:04I can see
00:09:06how many entries I have.
00:09:08Ok.
00:09:10So, we discussed about chrome.
00:09:12Normally, matrix is
00:09:14written as M into N.
00:09:16What do you understand by M?
00:09:18You understand by
00:09:20series.
00:09:24And you understand by
00:09:26columns.
00:09:30Ok?
00:09:32You understand by columns.
00:09:34I have given you 3 ways to express it.
00:09:36One is by 3rd bracket.
00:09:38The other is by 1st bracket.
00:09:40And the other is by double.
00:09:42So, you have to use these 3 ways.
00:09:44Now, I will
00:09:46write M cross N.
00:09:48I just told you about order.
00:09:50I have written
00:09:52an order here.
00:09:545 x 4.
00:09:56So, you have a matrix
00:09:58of 5 x 4.
00:10:00Here, we have
00:10:025 x 4.
00:10:04But, when we
00:10:06say it in words,
00:10:08it is written as
00:10:105 x 4.
00:10:12Do you understand?
00:10:14It is written in words.
00:10:16Ok.
00:10:18Now,
00:10:20think about it.
00:10:22I think,
00:10:24I will talk about this book.
00:10:26You tell me,
00:10:28what is my number?
00:10:30Yes,
00:10:32it is correct.
00:10:36These are MCQ.
00:10:38In this chapter,
00:10:40there are some theoretical things.
00:10:42MCQ is very important.
00:10:44So, I am discussing these.
00:10:46Exactly.
00:10:50You have told many things.
00:10:52Arifa,
00:10:54Masuma.
00:10:56This is our first character.
00:10:58This is our first character.
00:11:00And this is our column number.
00:11:02Keep this in mind.
00:11:04Character means
00:11:06the numbers in the order of
00:11:081, 2, 3, 4, 5.
00:11:10And column number is
00:11:1298.
00:11:14So,
00:11:16how can I express
00:11:18this 98?
00:11:20I am looking for
00:11:22my 98.
00:11:24I can say,
00:11:2698 is my character.
00:11:28Now,
00:11:30this is my first character.
00:11:32So, I will give 1.
00:11:34And this is my third column.
00:11:36So, I will give 3.
00:11:38This is 1, 3, 9, 9.
00:11:40This is 1, 3, 9, 9.
00:11:42This is
00:11:4498.
00:11:46Now,
00:11:48I will ask you
00:11:50to tell me
00:11:52this 99.
00:11:54How can I write this?
00:11:56Please tell me.
00:12:045, 9, 32.
00:12:06This is
00:12:1042.
00:12:12Let me check.
00:12:141, 2, 3, 4.
00:12:16I will give 4.
00:12:18And this is
00:12:202.
00:12:22So,
00:12:24this is
00:12:2692.
00:12:28So,
00:12:30how can I express
00:12:32this 92?
00:12:34I will use
00:12:36this I.
00:12:42I means
00:12:44body position.
00:12:52J means
00:12:54column position.
00:13:00Is it clear?
00:13:02Now,
00:13:04let's talk about the rectangular matrix.
00:13:06You can understand
00:13:08by listening to the story of Aritaka.
00:13:10Here,
00:13:12the origin and origin will not be same.
00:13:14They will be different.
00:13:16The origin and origin of the matrix
00:13:18is the body and column.
00:13:20So, in this matrix,
00:13:22the body and column will be different.
00:13:24The body
00:13:26and column
00:13:28will be
00:13:30different.
00:13:34They will not be same.
00:13:36I told you a story a while ago.
00:13:38I wrote a big rectangle
00:13:40and a column.
00:13:42You can write it mathematically
00:13:44in short form.
00:13:46M and N will not be same.
00:13:48What does M mean?
00:13:50M means the rectangle
00:13:52and N means the column.
00:13:54Let me give you an example.
00:13:56Look at this.
00:13:582, 3, 0,
00:14:004, 2, 1.
00:14:02Tell me
00:14:04how many columns are there in this matrix?
00:14:16Tell me
00:14:18how many columns are there in this matrix?
00:14:28Look at this.
00:14:32In this matrix,
00:14:34I have 2 bodies
00:14:36and 3 columns.
00:14:38So, I have a 2x3 matrix.
00:14:42Ishtiyak, Fareeha,
00:14:44Nirdoy, Masuma, Srikanth,
00:14:46Rajdeep,
00:14:48Thank you so much.
00:14:50Tasphia, Tanisha,
00:14:52Elamuni, Tahasan, Fareeha,
00:14:54Very good.
00:14:56This is a 2x3 matrix.
00:15:00Now, look at this.
00:15:02This is Ayutthaya's matrix.
00:15:04This is a Borgo matrix.
00:15:06You know that
00:15:08the number of bodies and columns
00:15:10will be same.
00:15:12Let me give you an example.
00:15:142, 0, 5, 3.
00:15:16This is a 2x2 square matrix.
00:15:22Now, let's see
00:15:24this is a row matrix.
00:15:26In a row matrix,
00:15:28my main priority will be
00:15:30row.
00:15:32My main priority will be
00:15:34body.
00:15:36The number of bodies
00:15:38will be same.
00:15:42When I talk about a body matrix,
00:15:44I have only one body.
00:15:46I don't care about the number of columns.
00:15:50The value of m
00:15:52will be 1.
00:15:54Let me give you an example.
00:15:56I have a matrix.
00:15:58It is a B matrix.
00:16:00The number of bodies
00:16:02will be 1.
00:16:04The number of columns will be 5.
00:16:062, 3, 4, 5, 6.
00:16:08The order of this matrix
00:16:10will be 1x5.
00:16:14The number of bodies will be 1.
00:16:16Now, let's see
00:16:18a column matrix.
00:16:20The number of bodies will be same.
00:16:22The number of columns will be 1.
00:16:24How can I express this?
00:16:26n is equal to
00:16:281.
00:16:30Now,
00:16:32let's take an example.
00:16:34This is a B matrix.
00:16:36The number of columns
00:16:38will be 1.
00:16:40The number of bodies will be 3.
00:16:425, 2, 1.
00:16:44The number of columns
00:16:46will be 1.
00:16:483x1
00:16:50is a column matrix.
00:16:52The number of bodies
00:16:54will be 1.
00:16:56The number of columns
00:16:58will be 1.
00:17:04Now, let's talk about
00:17:06the main root.
00:17:08The main root
00:17:10will exist
00:17:12when I talk about
00:17:14the B matrix.
00:17:16The main root will exist
00:17:18when I talk about
00:17:20the B matrix.
00:17:22The main root will exist
00:17:24when I talk about
00:17:26the B matrix.
00:17:28The main root will exist
00:17:30when I talk about
00:17:32the B matrix.
00:17:38Let's take an example.
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