Engineering Mathematics 07 | Linear Algebra: System of Homogeneous Equations | GATE All Branches

[@yoshianuragtesla8752]

00:02 Discussion on System of Homogenous Equations 02:00 Introduction to Homogeneous Equations 06:47 Homogeneous system of equations will always have at least one solution 09:23 Homogeneous equations always have consistent solutions 14:33 Solving for non-trivial solutions in square matrices 16:39 System of Homogeneous Equations solution with variable substitution 21:26 Row echelon form determines number of independent solutions. 24:40 Understanding independent and dependent solutions in linear algebra 30:19 Rank of augmented matrix is related to the rank of the argument matrix 32:03 Understanding the importance of rank in Homogeneous Equations 38:05 Understanding the relationship between rank of A and determinant being zero 40:33 Calculation of system of homogeneous equations 44:56 Solving system of homogeneous equations 47:07 Interview experience with marking scheme for GATE 50:12 Importance of confidence in answering system of homogeneous equations 51:52 Introduction to System of Homogeneous Equations 56:07 Understanding the concept of linearly independent solutions in the context of matrix 58:24 Importance of I Can Values and I Can Vectors in Linear Algebra

[@shivanipandey8120]

Thnx bro

[@satejgujar3023]

I can vectors nahi bro Eigen vectors... Btw Appreciated your efforts❤

[@KashishKashyap-db8ly]

At 34:55 why the solution is consistent and trivial? As we only know that rank of A is equal to rank of AB but it is not mentioned that the no of variables are also 5. According to this it may have consistent but non trivial solution

[@whoknows7701]

58:31 Answer should be option D, as rank + nullity = order of matrix, here order of matrix is (n+1) not n, which gives nullity = n which denotes no. of independent solutions. 🙂

[@raghavdolyar4984]

Correct hai bhai

[@raghavdolyar4984]

Tumhara answer correct hai

[@KhushiKumari-ot8kj]

Who is watching it in October

[@AmarjeetPrajapati-ks3um]

Question no. 7 ka ans -2 aa raha hai

[@naveenkumarnainola1584]

Me 😂😂

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App kon se sem me ho

[@Heavy_driver009]

26 dec 2024.....

[@vaibhav7453]

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[@monikasoni2739]

Thank u sir for your motivation and obviously your wonderful class

[@SailajaSahoo-i7x]

aap sir ki behen ya relative ho kya??? soni hai aapka title isiliye....

[@monikasoni2739]

No......

[@AnkitKumar-kz3mm]

34:57 sir for trivial solution rank(A)=rank(A:B)=no of unknowns in system of equations. But in question it hasn't been given no. of unknowns. So how can we say it is trivial or non trivial. Correct me please if I'm wrong.

[@kdgaming3924]

agar rank(A)= n= rank(A:B) hoga to independent rows zero hoga nah

[@saa6390]

Yaa, I have the Same Doubt....

[@saa6390]

@@kdgaming3924 yha jo sir ne 'n' use kiya hai... Wo "no.of rows" dikha rha... But trivial solution hone ke liye jo "n = no. Of unknowns" Hote hai.... Aur dono 'n' alag alag hai, dono me koi relation to hai nhi...!!! That's why this doubt arises...

[@nsoumik1711]

5*5 matrix is given bro. That’s sufficient to tell that there are 5 unknown.

[@saa6390]

@@nsoumik1711 bro 5×5 matrix se no. Of unknowns nhi cofirm hota hai bhai, usse bss no. Of equations pata chlta hai, that yaa there will be 5 equations... But those 5 equations can be made with the help of either 5 variables or 4 variables or 3 variables or even 2 variables also... Hope u understood the problem...

[@aardhya1082]

Dpp ke kucch ans match nhi kr rhe ..... 2)a ,3)a ,4)c

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[@virajsinghbhutoria]

Hello I am new to this channel, followed this course since lecture 1, really helping me. I gave gate EC in 2023; qualified but want to improve my rank so I am willing to join GW courses How can I get access to dpps and questions of gw?

[@nareshsharma5903]

Bhai app pe hi sab milega

[@suryakantluha6265]

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[@Anjalisharma-vr6pw]

Where the dpp? Please tell us that is helpful for us

[@prasanthkumar6393]

Love you sir 😗❤️

[@arnabdaw2587]

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[@rajshripal848]

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[@sangeetaambare7716]

Sir dpp mil nahi ahi hai plz batado kaha milegi

[@AbhishekBiharWala_]

Thank you sir ❤️

[@nafeesalam7929]

Thanks sir

[@indigoindigo6983]

9:32 That's not correct sir. A matrix X is equal to another matrix Y only if they are of equal order and xij = yij for all I and j. Here, there is an extra column in the augmented matrix. [A:B] cant be equal to [A]. Please correct me if I am wrong.

[@saa6390]

Yaa, u are right... I think that's just a way to to explaining and let us understand 😅😅

[@Techforyou__07]

Simulteneas equation par ek video banaye sir

[@continnum_radhe-radhe]

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[@yogeshkharb8292]

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[@indigoindigo6983]

10:16 With all due respect, trivia ka matlab ye nahi hota hai, as far as I know. Trivial meaning of very little importance or we might say, unimportant in our case. Har ek homogeneous system of linear equations ka ek solution (0,0,0,...,0) hota hai, jisko trivial solution bolte hain. And this sol is unimportant. Please correct me if I am wrong.

[@piyushjha757]

bhai maths class hai english class nahi

[@indigoindigo6983]

@@piyushjha757 Math ki book me english ka koi word nahi dekha kya kabhi?🤔🤔🤔 Or agar english itni hi unimportant hai, to likh kar dikhao saari math terms ki definitions math me hi, bina koi dusri language use kiye.

[@piyushjha757]

@@indigoindigo6983 toh tum jee aur gate jaise examinations mein defintions yaad kar ke jaoge . Sahi hai phir maths ko rehne do english ko hi pakar lo. Important hona aur priority rakhna mein difference hota hai english important hai but filhal maths se important toh nhi ho jayega na

[@deeyakaur]

Yes ur right, but I think it's just a nice example to help remember. If u want something more accurate, then u can use the original latin definition of trivia, which meant the meeting point between 3 roads. In this case the meeting point is with all of our variables at a single, unique solution :)

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[@devanshtanwar28]

Ni aaya samjh 27:45

[@वैदिकरसायन]

❤

[@AbhinavJha03]

done on 3 jan 2024

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Semester wala attendance lagega

[@national_study_in_bangla_697]

thank you sir

[@takshpatel8109]

Thank you sir.