🔷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]

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[@SkanCityAcademy_SirJohn]

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[@petermarcus6475]

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[@SkanCityAcademy_SirJohn]

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[@petermarcus6475]

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[@SkanCityAcademy_SirJohn]

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[@ENOCK-t5u]

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[@SkanCityAcademy_SirJohn]

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[@rhe7187]

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[@SkanCityAcademy_SirJohn]

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[@davidbanahene307]

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[@SkanCityAcademy_SirJohn]

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[@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]

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[@SkanCityAcademy_SirJohn]

Thank you so much. Enjoy your stay on the channel

[@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

[@ChikweJecinta]

You just save a life 😌 Thanks

[@SkanCityAcademy_SirJohn]

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[@ChikweJecinta]

@@SkanCityAcademy_SirJohn yes am a Nigerian

[@SkanCityAcademy_SirJohn]

Okay...

[@SkanCityAcademy_SirJohn]

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[@BlunT402]

Very helpful 👍

[@SkanCityAcademy_SirJohn]

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[@OriaPlay]

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[@SkanCityAcademy_SirJohn]

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[@BetyBaysa]

Nice

[@SkanCityAcademy_SirJohn]

Thanks

[@tirupatichitralekha7488]

Really superb sir

[@SkanCityAcademy_SirJohn]

Aww thanks so much

[@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.

[@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

[@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

[@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]

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[@ADendane]

Thank you.

[@SkanCityAcademy_SirJohn]

Youre welcome

[@bonyevitus8979]

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[@SkanCityAcademy_SirJohn]

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[@tamilmahi8744]

Super

[@SkanCityAcademy_SirJohn]

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[@kalpanamaths9645]

Is n mention only columns

[@SkanCityAcademy_SirJohn]

I don't get the question

[@chisomomkwanda8161]

Let me subscribe.

[@SkanCityAcademy_SirJohn]

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[@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