Kernal(A) is nothing but it is the (non-trivial) solution space of Ax=0. (This Ax=0 is called the homogenous system of equations.) That is, there are infinite number of non-trivial solutions of Ax=0. Collectively they (infinite solutions) are called Kernal of A, i.e. ker(A). NB: trivial solution of Ax=0 is a unique known solution, x=0. For Ax=b (non-homogeneous system of equations, where b is non-zero vector), if there exists kernal(A). (It means there are non-trivial solutions for Ax=0.) In this case, collectively these infinite number of solutions is also called null space (i.e. kernel(A)) of Ax=b. This is the case if Ax=b is consistent non-homogenous system of equations. For inconsistent Ax=b there is no solution of x at all in theory!
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Such a pretty teacher and having excellent sense of knowledge.
So can we say that kernel of a matrix is same as finding the nullspace ?
Yes
😊
Kernal(A) is nothing but it is the (non-trivial) solution space of Ax=0. (This Ax=0 is called the homogenous system of equations.) That is, there are infinite number of non-trivial solutions of Ax=0. Collectively they (infinite solutions) are called Kernal of A, i.e. ker(A).
NB: trivial solution of Ax=0 is a unique known solution, x=0.
For Ax=b (non-homogeneous system of equations, where b is non-zero vector), if there exists kernal(A). (It means there are non-trivial solutions for Ax=0.) In this case, collectively these infinite number of solutions is also called null space (i.e. kernel(A)) of Ax=b. This is the case if Ax=b is consistent non-homogenous system of equations. For inconsistent Ax=b there is no solution of x at all in theory!
This was an amazing explanation. Thank you so much for this :D
Tonnes of thanks!! 🙏🙏🙏
Great lecture madam,,I just got that right in my 2nd yr degree level,,
You liked this video and we felt happy to know this, if you subscribe and share this channel as much as possible, we would love to work harder to make more content like this .
Thank you soo much
Ganesh institute
Thank you!!
Nice explanation 👍
Fantastic explanation 💗
Mam kitni rows ko zero banana hai
but for Ax=0, doesnt x need to be 4 x 1 since A is 3x4?
this video is very usefull
Yu ar so gorgeous and your teaching process is very good
thanks a ton
What is the intuition of kernel
[A:0]argumented matrices
Plz upload more videos on linear algebra.plz
Thank You for your help mam.
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Thank you
Why we no change the x part
Good sir
bruh
Can you again solve this in easy method
Thanks mam
I did not understand mam
Bhai vala acaha ta Subham(+2 friend
You are very beautiful woman. I accept that fact. Can u discuss Kernel Trick please?
But
hindi me hi theek h !!!
I think it's a complicated way
Show a better one.
oook
nice
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Smart miss Hindi mai licture deya karooo yarrr
Pls remove subtitle in video, it's hiding the solution and ur explanation
You can hide them by yourself by clicking on cc
Haaq tum sy Qoi sabak seek jai gaaa
Not clear to me. She is good looking but not a good teacher.
Hello smart miss please in urdu
pankha bad kr liya karo mam ya fir acha mic lelo