Це відео не доступне.
Перепрошуємо.
Rank of a Matrix: Maximum number of linearly independent row or column vectors.(see pinned comment)
Вставка
- Опубліковано 20 тра 2021
- Row Rank is defined as: Maximum number of Linearly independent row vectors.
Column Rank is defined as: Maximum number of Linearly independent column vectors.
Theorem: Row rank of a matrix is always equal to Column rank of a matrix.
Thus,
Rank of a matrix is defined as row rank = column rank of a matrix.
Row Rank is defined as: Maximum number of Linearly independent row vectors.
Column Rank is defined as: Maximum number of Linearly independent column vectors.
for the last question:
rank is three and 1st,3rd and 4th row will be linearly independent.
thanku sir
Great..
Thank you for posting your answer 😊
Great explanation thank you
Thank you and welcome 🙏 🙂
Thanks Bro It was helpful.
Welcome:)
pl explain bit more clearly on how to know if two rows are linearly indepndent,is it like if we multiply a row by a number we get the other row.
Yes..correct
@@DrMathaholic does that mean if the first row is (2,3,5) and the second (4,6,10),then they are dependent i.e 2(2,3,5)= ((4,6,10) or it has some extra logic.
@@sachinrath219 yes..what you wrote is correct!!
If a vector can be obtained from other vectors by some linear combination then those vectors are linearly dependent.
@@DrMathaholic hope some 'linear combination' means all the elements of a row are to be multiplied by a particular number only like I took 2 as an example.
Consider the system of linear equations AX=B ,then which of the following is true.
1)AX=B is homogenous if B=0
2)if B=0 then detA is not equat to 0 and and x=0 is the solution of AX=B
3)the equation AX=0 has a non trivial solution iff detA=0
4) All of these.
Please which is ryt option 1 or 4
1st option is correct. 2nd option is incorrect, detA may or may not b 0.
If A is given to be square matrix then 3rd option is also correct
Thanks
@@nighatlone77 welcome!!
pl intimate how to know which ones should be zero in a 5 x4 matrix for gauss elimination method,i have seen videos where they just tell these should be zero but did not explain why those positions should be zero,thanks.
Nice question. It requires a detailed answer. I will try to type over weekend
@@DrMathaholic can u share ur whatsapp no so that i can give a que on gauss elimination what m unable to do,thanks.
@@sachinrath219 pls email me jatinmajithia@gmail.com
@@DrMathaholic have mailed the question,pl go thru,thanks.
sir,have mailed a question,pl go thru,thanks.
Air please give answer of these questions
1. No of linearly independent vector
2. Dimensions of soln space
3. Dimensions of null space
4.No. of free variable
5 no of linear independent soln
6 no of lineary independent variable
I'm facing difficulties in finding difference blw these..
For which matrix you are having these doubts?
You take any non zero row. It is always lin ind. Does it mean that rank is 1 for all nonzero matrices???
That need not b linearly independent
@@irshadsirslectures4446 what need not be lin ind? All I insist is understand the difference betn no. of and max. no. of. They are different.
@@charusheeladeshpande3717 u mean if we take a mtrx , then a non zero row is L. I
Awesome session
Thanks 😊
Hello sir please tell
What is the relation between rank of matrix and independent vectors in vector space
Reply sir
If you have n vectors and you want to check whether they are independent then simply write them column wise,you get a matrix and now find the rank of this matrix if it is n then vectors r independent else dependent
how to find the maximum number?
If you have matrix of order 10x10 and suppose that, when you do row operations you get 4 non-zero rows.
Then question is what is the maximum number of non zero rows?
Answer is 4.
Thus 4 will be the rank of that matrix.
No. Maximal no. of lin ind rows is the row rank.
Yee, I should have been little more cautious.
Row rank is maximum number of linearly independent row vectors. Same for column rank
Sir actually I didn't get that ,,,,how to find column rank ,
Sir please help me 🙏
Could you please explain it to me
Hi
Try to see again from 9:00 to 10:00 time frame.
After doing row operations simple see how many pivot entries are there.. that is your column rank that means see how many leading non zero entries you have
Or if it's difficult then simply find row rank bcoz row rank is always equal to column rank
if A is a 5*7 matrix with all its entries equal to -1. The rank of the matrix.....please answer it
As all entries are -1 so all rows and all columns are same. That means we have only one independent row/column and all other rows / columns are 1 times the that row/column. Thus rank is 1.
If A is 3*4 real matrix and AX=B is an inconsistent system of linear equations. Then the highest possible rank of A is
@@nighatlone77 no solution means r(A) not equal to r(A|B) , if r(a)=3 then obviously r(a|b) is also 3 and we will have a solution. IF r(A)=2 then we may have r(a|b) =3 and hence inconsistent.
So max possible rank of A can be 2
Thank u very much
Why maximum number of l.i. row = maximum number of l.i. column? Sir please help me
It's a long proof. Column rank = row rank.. difficult to type here. You can search online. If any step is unclear then you can ask me...
Ok sir
Answer : rank of Matrix =2
Linearly independent row vectors = (1 2 3 4) (7 3 4 2)
Linearly independent column vectors=(1 3 7 0) (2 6 3 0)
Thank you Dhoni's fan for posting the answer 😀
@@DrMathaholic 😂👍