🔷12 - Rank and Nullity of a given Matrix (Row Echelon Form)

[@rashidissa5887]

I'm a new student in matrices but can find determant and values of the unknowns in a linear equation. But this lesson is beyond my compression. Perhaps my age? I'm 79 and did my O-Level in 1967 Cambridge. But I still can't keep distant from maths.Comming across such tutors makes me even more crazy on the subject. Greetings from Zanzibar

[@SkanCityAcademy_SirJohn]

Wow. I'm really impressed. I'm short of words. You have really encouraged me so much. Thanks so much

[@SkanCityAcademy_SirJohn]

@@petermarcus6475 no please, English

[@petermarcus6475]

@@SkanCityAcademy_SirJohn I really appreciate your work tomorrow I have my final and with this clear explanation I really understood very fast thanks and may God bless you.Just got a new subscriber

[@SkanCityAcademy_SirJohn]

@petermarcus6475 aww thanks so much and good luck.
Where do you watch me from?

[@petermarcus6475]

@@SkanCityAcademy_SirJohn am in Cyprus but I am a Tanzanian 🇹🇿

[@ENOCK-t5u]

We appreciate your service

[@SkanCityAcademy_SirJohn]

Thanks so much

[@BabatopeFagbenle-rk6jy]

You are clear as my heaven. Good job gauss and Jordan will be proud of you.

[@SkanCityAcademy_SirJohn]

Thanks so so much

[@rhe7187]

That's the best video I got on this topic

[@SkanCityAcademy_SirJohn]

Thank you very much

[@davidbanahene307]

Awesome. Great job so much clarity

[@SkanCityAcademy_SirJohn]

Thanks so much

[@OriaPlay]

Marvelous work! U have really worked on your camera. Kudos 💯

[@SkanCityAcademy_SirJohn]

Thanks so so much

[@malekahlologelo5316]

Why do u leave your Row Echelon Forms incomplete? You still perform the row operations to simplify further.

[@SkanCityAcademy_SirJohn]

Incomplete in which way, kindly come again with your question, there is a difference between row echelon form and reduced row echelon form. Kindly note the difference. The idea is to produce the echelon form of the matrix and to count the number of non-zero rows, that gives the rank

[@menglishspeaking2405]

For sure you know how to deliver a lesson, explain kernel and image of transformations

[@rahmandesigns]

Please teach how to find eigen values of 3x3 matrix

[@SkanCityAcademy_SirJohn]

Okay

[@menglishspeaking2405]

I love your teaching you are good at , best guider . facilitator ,good motivators,you have unique methodology of teaching.just keep it up help us to find kernel image and dimensions

[@SkanCityAcademy_SirJohn]

Thank you so much. Enjoy your stay on the channel

[@ChikweJecinta]

You just save a life 😌
Thanks

[@SkanCityAcademy_SirJohn]

Aww...thanks so much. Are you a Nigerian?

[@ChikweJecinta]

@@SkanCityAcademy_SirJohn yes am a Nigerian

[@SkanCityAcademy_SirJohn]

Okay...

[@SkanCityAcademy_SirJohn]

Can we chat on WhatsApp?

[@BlunT402]

Very helpful 👍

[@SkanCityAcademy_SirJohn]

Thanks so much

[@BetyBaysa]

Nice

[@SkanCityAcademy_SirJohn]

Thanks

[@tirupatichitralekha7488]

Really superb sir

[@SkanCityAcademy_SirJohn]

Aww thanks so much

[@tluangainfimate4421]

You said all the diagonal element should be 1 and at the end the last one is zero please explain sir?

[@SkanCityAcademy_SirJohn]

Yes, I said that, and also said that if the is a row that has all zeros, it should be at the bottom of the matrix

[@habeebsalaudeen]

What if the matrices with linear dependence are not the same?

[@SkanCityAcademy_SirJohn]

Actually the linear dependent rows will not be the same, the values will be different, but then it will be a scalar multiple of another row in the same matrix.

[@ADendane]

Thank you.

[@SkanCityAcademy_SirJohn]

Youre welcome

[@bonyevitus8979]

U just save a life.. I owes u so much in dis semester else it would be 🔥😂

[@SkanCityAcademy_SirJohn]

Awww, I'm so grateful

[@oulafatla8686]

what is linearly independent rows/columns?

[@SkanCityAcademy_SirJohn]

Linearly independent row or column is a row or column whose elements are not a constant multiple of another row or column.
Eg if column 1 has = 1, 2, 3
Column 2 = 5, 10, 15 and
Column 3 = 5, 9, 13.
C2 is a linearly dependent on c1, because it is formed by 5*C1
But C3 is linearly independent on C1

[@peace75084]

why are there only 1 linear combination of rows?? there is C2 =2C1 and also C3 = 2C2..so there are 2??

[@SkanCityAcademy_SirJohn]

The reason being that for
1. Rows: the two rows depend on each other R1 = 1/2 of R2 and
R2 = 2 of R1. Since both rows can be written as a linear combination, the max no of linearly independent rows is 1.
Column: the three columns depend on themselves
C1 = 1/2 of C2, = 1/4 of C3 and so on,
Since the three columns can be written as a linear combination of the other, the max no of linearly independent columns is one.

[@peace75084]

@@SkanCityAcademy_SirJohn 👍

[@tamilmahi8744]

Super

[@SkanCityAcademy_SirJohn]

thanks so much

[@kalpanamaths9645]

Is n mention only columns

[@SkanCityAcademy_SirJohn]

I don't get the question

[@chisomomkwanda8161]

Let me subscribe.

[@SkanCityAcademy_SirJohn]

thank you so much for your subscription

[@asaredurowaadoris195]

Pls it at the end of doing the row echelon you get something like
1 -2 6
0 0 0
0 0 0
Pls wat will be the rank

[@SkanCityAcademy_SirJohn]

The number of non-zero rows is 1, so the rank is 1

[@asaredurowaadoris195]

Thank you

[@SkanCityAcademy_SirJohn]

You are most welcome