YT YouTube2Text

YouTube2Text → Transcripts → Chapter 01: System of linear Equation and Matrix V2

Chapter 01: System of linear Equation and Matrix V2 — Transcript

by Institute of Digital Technology - IDT · 3,326 words · 622 segments · language en · Watch on YouTube

Open in transcriber Summarize with AI Download SRT/VTT

Full transcript

0:00foreign
0:00[Music]
0:09we talk about the system of equation
0:11algebraic procedure
0:14outcome
0:16in our system equation you can use
0:19Elementary operation to find solution to
0:23a linear equation
0:27the next point you can find row Echelon
0:29form and reduce row Echelon form from a
0:32matrix
0:35determine whatever system of linear
0:37equation has no solution unique solution
0:40and an Infinity number of solutions from
0:43each row each landform
0:46so a system of equation using gaussian
0:49elimination or both your tongue
0:51elimination
0:53model or physical system with linear
0:56equation and tensor
0:58so this is the way that you can solve
1:01about the system of linear equation you
1:04have five way
1:05to Seoul and when you study metric you
1:09can solve the system or linear equation
1:10by inverse metric also
1:13in your class now it is not only by
1:16substitute
1:17by addition and by graph you can solve
1:24sum of system equation by Elementary row
1:27operation by row Echelon form by
1:30gaussian by goshok long or by
1:37you have more about this one so about
1:41the system of linear equation
1:44and
1:46we have take an in-depth look at
1:50graphical representation of system of
1:53equation
1:54as well how to find possible solution
1:57graphically
1:58our attention now is turned to work with
2:01system algebraically
2:05definition of system of linear equation
2:08a system of linear equation is a list of
2:11equation so when you write
2:16a 1 1 x 1 plus a 1 2 x 2 equal to B1 so
2:22this is only equation
2:26we call this this equation
2:29when you write in list
2:31this is one equation one equation two
2:34and equation m
2:37because from 1 to M this is m
2:40equation
2:43M equation you write in a list we can we
2:47can call this we cannot call this system
2:49equation we call this is the system of
2:52linear equation you can write in curly
2:55blanket or you can write in the list of
2:57uh equation we call this is the system
3:00of unique way equation
3:04uh where a i g AIG so I is
3:11uh like row
3:14and J this is like column
3:19killer muscle
3:20so this is
3:24AIG it means that the position of
3:28uh a that stand in row I and column J
3:34and BJ are real number so a
3:39and B is real number is belonged to
3:43real number
3:45the ball of system of M equation in the
3:48in the N word variable
3:52X1 X2 and T2 x n this is n variable
3:57so we can write in this form
4:00from this
4:01system linear equation we can write to
4:04this one
4:06is Sigma J from 1 to n a
4:10a i j x j equal to b i
4:13is from one two three four until m
4:20and that is related to our system
4:24equation
4:25this is system equation none
4:32homogeneous
4:35uh homogeneous
4:39this is the system of linear equation
4:43non-omogenous because the right hand
4:45side it is not equal to zero
4:48if it is not equal to 0
4:52this is non-omogeneous system of linear
4:55Equity equation
4:58and homogeneous system of linear
5:01equation this form
5:03it means that the right hand side
5:06this is equal to zero it means that b i
5:11if b i
5:13I from 1 to m
5:16equal to 0
5:18this equation we can call the system
5:20equation we can call
5:22the system of homogenous system of
5:25equity equation
5:29uh aij
5:32Alia scalar scalar it means that this is
5:37constant number
5:39and X I already variable
5:44so the
5:46consistent and inconsistent
5:51so please remember that point what is
5:55consistent
5:56and what is inconsistent
5:59system equation
6:04system equation
6:07now a system of linear equation is
6:11called consistent if there exists at
6:14least one solution
6:17so the system that have only one through
6:20at least one solution at least one
6:23solution it means that
6:25have one solution two solution three
6:29solution or more than three or Infinity
6:32solution
6:33at least you know at least at least it
6:36may not start from one
6:38can be one two three and four until two
6:41Infinity
6:43so if the system or linear equation
6:46have at least one solution we can call
6:49the system is consistent
6:51we can call consistent
6:55this is consistent
6:57if the system have no solution
7:01if the system have no solution we can
7:05call this system of linear equation this
7:08is inconsistent
7:10consistent it means that have at least
7:13one solution
7:15inconsistent it means that has no slow
7:17no solution so this is the opposite
7:21between consistent and inconsistent
7:24consistent it means that you have
7:27at least one solution and inconsistent
7:30you have
7:33no slow no solution in here
7:38uh
7:39Elementary row operation
7:42so now we will talk about the element
7:44three row operation
7:48Elementary over row operation is begin
7:50this section with an example
7:54example verify
7:57an order pair of a solution
8:01algebraic verify that X and Y minus 1
8:05and 5 is a solution of
8:08a system of equation is here which I
8:12explained you from a bio point we have
8:16equation One X Plus y equal 3 and Y
8:19minus x equal to Phi the intersection
8:22between Line 1 and line two at the point
8:25x 0 equal to
8:27negative 1 and y 0 is equal to 4.
8:32424
8:33so this solution is like
8:36example you use about
8:39equation one
8:41equation one you use x equal to -1 and y
8:46equal to four this is equal to 3.
8:49and equation two is also you use uh our
8:53equation one is
8:55X Plus y equal to 3 and Y minus a equal
9:01to 5.
9:03equal to Phi
9:05so now you got this point in uh when you
9:09start to shoot when you substitute
9:12negative one and four
9:15negative one and four into equation 1
9:18and into equation two you got
9:21equation one is X plus three plus y
9:25equal to 3 is true
9:28true because
9:30minus one plus four
9:32equal to 3 and
9:35y minus x equal to 5 also true
9:40because uh 4
9:43uh minus and minus 1 equal to 5. so
9:48a equal to negative one and five and y
9:53equal to 4 this is a solution of our
9:56system in the aqua equation
10:01so now we got this is
10:04system or linear equation have only one
10:06solution negative one and four
10:11and Elementary row operation
10:14Elementary Pro operation Elementary
10:17operation are those operations
10:19consisting
10:21of the following
10:24the first you can interchange the other
10:28in each patient at least
10:31example in here
10:33you have uh X Plus y equal three
10:39and Y minus X
10:42equal Phi so you can write y minus X
10:46equal Phi and
10:50x minus y equal to 3. so this is in the
10:54chain Row in our list you can change
10:59and point two multiply an equation by
11:02non-zero none's row number
11:05so in here this is also you can
11:09uh multiply
11:12example I write uh
11:155y minus pi x
11:19equal to 25 and
11:23uh
11:2510 x
11:27plus 10 y equal to 0 30. so I can
11:31multiply an equation with non-zero num
11:35non-zero number
11:38and replace an equation with its cell at
11:422 multiply another
11:44uh
11:47equation it means that example
11:50I have X
11:52plus y equal to 3 and X
11:55minus y equal to Phi
11:58so in this here I done one I don't want
12:01to uh
12:05I don't want to
12:07add equation one and equation two so I
12:10write this one is
12:11multiply with negative one I got X Plus
12:14y
12:16equal to 3 and
12:18Negative X
12:20plus y equal to minus 5. so I can
12:23addition this is 2X
12:26equal to minus minus four so X
12:302 y equal to
12:33uh
12:35the place that you you think it means
12:38that minus one this is plus and minus so
12:41this is only uh minus two you got minus
12:46two so you got y this is
12:49equal to the point that you think
12:53the point the other uh solution that we
12:56want to make we want to find in this
12:58area
13:00and
13:02it's important to not
13:04that none of this operation will change
13:07the set solution of the system equation
13:11so when you
13:13exchange about the role
13:17to
13:18Row 1 and Row one to Row 2 and Row 2 to
13:21row three or Row one row two you get
13:24from
13:25row two
13:28plus k ro1 and something so our solution
13:32it is not the same solution it is not
13:35uh another solution in here please
13:39remember that not change about the
13:41solution when you interchange order in
13:44which equation list multiply in the
13:47equation by none's row or replace
13:49equation with its cell add to a multiply
13:52of a multiple of another equation so it
13:56is not changed
13:57it the same solution
14:02example effect and Elementary operation
14:06so that the system
14:09X
14:10Plus
14:11y equal to 7 and 2x minus y equal to a
14:18has same solution as system X Plus y
14:22equal to so n and negative
14:273y equal to 3x
14:30so
14:31they want you to show us about this
14:34system equation and this is some system
14:37equation have the same slow solution
14:42so notice that the second system has
14:45been obtained by taking the second
14:48equation of the first system
14:51-3 minus 2 time
14:54first equation as this one
14:58so
15:00it means that the second question
15:03get from
15:05get from
15:07the first system adding
15:10the first system adding two
15:13time on the first equation
15:16to time on the cross equation so this is
15:19first equation
15:21and per system so I add two time to time
15:25it means that
15:26this is multiplied by minus two
15:30so I got minus 2X
15:33uh minus 2y equal to minus 14. and this
15:39is 2x minus 2y
15:42equal to uh
15:45a
15:46equal to a
15:49so now we can check
15:52we can check this one it's all
15:55and this is for
15:58y equal to this one is like
16:03uh
16:04uh six
16:07minus minus six yeah
16:10so
16:12this one maybe
16:13four yeah is minus minus six
16:18so this equation
16:20this equation is
16:22get from the
16:24system one
16:27take the first equation multiply by
16:30negative 2 18 with the equation two so
16:34you got this result
16:37and for the next
16:44for the next verify this is
16:49and within the current equation is a
16:52second system now
16:54uh
17:002x negative y
17:06we got this one is four it's not uh
17:09three
17:11this is four
17:15negative 4.
17:19and now we check
17:23we check it means that X Plus y equal to
17:265 plus 2 is
17:287 and 2x minus y
17:33substitute x equal Phi and y equal to
17:36this is equal to eight so this is
17:40uh
17:41there is a I mean that it is certified
17:45left hand side and right hand side
17:49hang Phi and 2 is also a solution of the
17:53first equation
17:54of first equation
17:57so the next point we will talk about the
17:59elementary row operation and solution
18:03suppose you have a system of two linear
18:05equations
18:07we can let E1 equal to B1 E2 equal to B2
18:13and E2 equal to B2 E1 equal to B B1 so
18:18this is we can change each other
18:21and the next the point two
18:25we multiply equation two
18:29Vision Two by K
18:32by K
18:34but K it is not equal to 0 besides 0.
18:39K is provide K opposite of zero
18:43so three you got
18:47you can addition between equation 1 and
18:50equation two
18:51it means that
18:54uh
18:56you got about E2 plus ke1 equal to B2 uh
19:02plus KB case B1
19:07k
19:08including k equal to zero
19:12for an EK
19:14scalar okay including k equal to 0 also
19:17in here
19:19so now before we proceed with a proof of
19:25serum 1.8
19:28let us consider this serum in contact of
19:33our example
19:35E1 we let E1 is equal to
19:39X
19:41plus y B1 equal to 7
19:44E2 2x minus y
19:48and B2 is equal to X
19:51equal to a
19:53so now
19:55now we recall Elementary row operation
19:58we use to modify system in solution to
20:01example
20:03first we add
20:06we add
20:07negative two times
20:10the first equation to the second
20:13equation in term of
20:16uh serum 1.8 this section is given by
20:21it means that
20:22we add
20:24minus two times our first equation minus
20:28two times our first equation
20:30to time of first equation
20:35uh to the current equation so second
20:37equation you got the current equation
20:41get from
20:43second equation Plus
20:45negative time of
20:48equation equation one
20:51so this is meaning
20:53so now we got
20:57this
20:59equation E1 equal B1 and E2 minus two uh
21:04E1 equal to B2 minus uh
21:08B1
21:10so now we got
21:13we got E1 equal B1 and E2 equal to b e
21:17B2
21:20this is our result that we can check all
21:24together about this point
21:26and finally we can
21:30find one by one like B1 equal B1 and E2
21:34equal to B B2 or E2 plus ke1 equal B1
21:39plus K B1 so we obtain E2 equal B2 and
21:43E1 equal to B B1 in our receptify
21:50uh sold a system linear equation with
21:53Elementary operation
21:56so this is our system of
22:01uh
22:02linear equation so they want us to solve
22:05the system of linear equation with
22:07Elementary row operation find the
22:10solution to this the system
22:13so we can relate this system of
22:16serum 1 8 above in case we have
22:21we let E1 is equal to X Plus 3y plus six
22:25disease and B1 is equal to 25 E2 is also
22:29and E3 is also
22:32so now this is our equation
22:35this is our equation and this is our
22:39left letting
22:41but in the definition we can first
22:44replace the current equation by two time
22:47the first equation add to the second
22:50this year
22:52so it means that
22:55we can
22:59use we can use the second equation
23:02by replace the current equation by two
23:06time of
23:08first equation A2 second it means that
23:12you take this one divided by multiply by
23:16negative 2 and plus 2 equation two and
23:21plus through this equation
23:23so this one divided by 2 multiplied by
23:25negative 2 is 2X
23:28minus
23:306y
23:32minus
23:34well equal to minus 50.
23:37and 2x
23:40plus so when y
23:43plus 14
23:47Z equal to
23:4958 so you can add in is no X
23:53so this is uh
23:55so when y minus 6y is only y
23:5914 minus 12 is 2.
24:02to Z equal to a so we got this one
24:07now
24:08and also in
24:12equation 3 is only
24:142y
24:15plus pi Z equal to 9 19 is the the same
24:21here
24:22so now we can check for
24:26our replacement to equation two
24:29time second add to sir
24:33so now you got this is
24:37second
24:40answer so if you want to
24:44omit it y you can write 2y minus 2y
24:48minus 4 Z equal to minus 16.
24:53and this is 2y
24:55plus pi Z
24:57equal to 9 19 so it's no Y in here this
25:02is z equal to 3. so now we can check all
25:06together
25:07so Z is equal to 3 in here so this is we
25:12got about this is our equation system
25:14equation when you know the value of Z
25:17you can find about the value of y by
25:20substitute Z equal to 3.
25:23when you know the value of y in here I
25:26write y0 you can find the value of a
25:29fake because you know y you know Z so
25:32you can substitute the value of Z and
25:36you can substitute the value of y you
25:38got the value of object in here
25:42so this way they can call disease
25:45Elementary or pre operation or
25:48Elementary row Opera a row operation
25:51please remember about this point
25:54so you got set Z equal to 3 y equal to 2
25:59and x equal to 1 by our circuit
26:01substitute so
26:04solution of this equation is X Y and Z
26:07equal to 1 2 and 3.
26:12the process is callback subtit
26:14substitute alternative in one point when
26:18you could have
26:19continue as follow at
26:22negative two times the equation to
26:25second or then at six
26:28negative 6 times to turn to the first
26:32this is up to you so we also get the
26:35same solution
26:37x equal to 1 z y equal to 2 and Z equal
26:43to 3 also
26:44so all the point which I taught you
26:48today it means that I only talk about
26:50the system equation and how to solve the
26:53system of equation by changing into
26:56chain about the role or in the chain
26:58about the equation in our list or can
27:02multiplication
27:03none's row number in other equation and
27:08you can solve the system of linear
27:10equation by Elementary row operation
27:12so now we have continued to study about
27:16the uh how to solve the system or linear
27:20equation by ghost chin elimination
27:25in here
27:28now we can check for the next point for
27:31the next point
27:34now we go to gushing elimination
27:39what is gaussian elimination
27:41example when you have
27:44I will explain you in here
27:47when you have a x a 1 x 1 plus A2 A1 2 x
27:552
27:56and plus a13 X3
28:00equal to B1
28:03a21 X1
28:05plus a 2 2
28:07x 2 plus a 2 3
28:10x 3 equal to B2
28:14a31 X1 Plus
28:17a 3 2 x 2 plus a33
28:23take three equal to B B3
28:26so this is the form of
28:30uh
28:32system linear equation B if we want to
28:36find about the system of linear equation
28:38by gaussian elimination you we convert
28:41from this equation to H1 Matrix
28:54to H1 metric here
29:00to each one
29:03Matrix
29:04like H1 Matrix you just only write about
29:08the
29:09the constant in our system
29:11in our system
29:13so you can write a11
29:16a12
29:18a13
29:19and B1
29:22a21
29:24a tool
29:26a23 and B2
29:2981
29:3182 and a33
29:34is this B B3
29:37so when you got this H1 Matrix gaussian
29:40elimination is f the same
29:43a11
29:45a12
29:47a13
29:49B1 this one is zero zero and this is
29:53only I can call this is K
29:58and this is also K1
30:01uh
30:02is it p p and zero zero and also uh m
30:10equal to l
30:12Prime
30:14so this is
30:16the kind or the form of gushing eliminae
30:21which in a limitation or we can call
30:23this is upper triangular main metric or
30:27so so the next point you will know about
30:29this I will explain you this is only my
30:32draft or my shortest explanation how can
30:37you do a gaussian elimination with
30:39system of unique way equation
30:42now we can check this is only my
30:46explanation which I told you already
30:49when you want to so you should be
30:52changed from the system line equation to
30:55argument May a metric example this is we
30:58have about the system of unique way in
31:01the equation
31:02so this system can be right as a
31:04treatment Matrix as follow so this one
31:07yeah when we have the system of linear
31:10equation we can go to uh h1ma H1 Matrix
31:15H1 metric we can use only the
31:18coefficient of variable
31:20or you can say use only the constant of
31:24equation
31:25so this is the constant or coefficient
31:28of this one three six twenty two
31:34seven Fourteen and eighteen so this is 0
31:38x
31:39plus 2y so we have one
31:43we have three we have six this is 20 25
31:482
31:501 14 and
31:5358 and this is zero
31:56this is 2
31:58this is 5 and this is 8 9 19. so
32:04achievement Matrix you can take only the
32:06constant
32:08we can stand
32:11with our equation to write in
32:15this one in metric we call this is Row
32:18one row one this is row two and this is
32:22called row row three this is column one
32:27alarm 2 and this is Kalam column 3 also
32:32so when you want to find solution of
32:36equation by gaussian elimination you
32:38should be convert from
32:40system equation to the H1 Matrix Plus
32:45[Music]

About this transcript

This page contains the full transcript of Chapter 01: System of linear Equation and Matrix V2 by Institute of Digital Technology - IDT, generated from the public captions YouTube serves with the video. The transcript has 3,326 words across 622 segments, with the original timestamps preserved so you can click any line to jump to that moment in the embedded player.

What you can do with it

Use the transcript to take notes, quote the speaker, build a study guide, generate a summary with ChatGPT or Claude via the YouTube Summary tool, or export it as a timed subtitle file with YouTube to SRT. You can also re-open it in the transcriber to choose a caption track available on the video.

Free YouTube transcript tool

YouTube2Text is a free YouTube transcript generator — no signup, no daily limit. Paste any YouTube link and get the full transcript instantly, with timestamps, click-to-jump, caption language selection, AI prompts for ChatGPT, Claude, and Gemini, and exports to TXT, SRT, VTT, or Markdown.