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s3a
 2 years ago
Question:
If A is a 3 by 5 matrix, what information do you have about the nullspace of A?
Answer:
N(A) has dimension at least 2 and at most 5.
My trouble:
How do we know this?
s3a
 2 years ago
Question: If A is a 3 by 5 matrix, what information do you have about the nullspace of A? Answer: N(A) has dimension at least 2 and at most 5. My trouble: How do we know this?

This Question is Closed

ingenuus
 2 years ago
Best ResponseYou've already chosen the best response.0m>=r m=3 so 0=<r=<3 dim N(A) = nr=5r 2<=5r<=5

s3a
 2 years ago
Best ResponseYou've already chosen the best response.0You're using the notation where m is the number of rows and r is the rank, right?

ingenuus
 2 years ago
Best ResponseYou've already chosen the best response.0yes m=#rows n=#columns r=rank

s3a
 2 years ago
Best ResponseYou've already chosen the best response.0So m >= r always holds for the nullspace of a matrix?

ingenuus
 2 years ago
Best ResponseYou've already chosen the best response.0rank is #pivot rows right? can it be more than #of rows?

ingenuus
 2 years ago
Best ResponseYou've already chosen the best response.0it is just a fact for every matrices

ingenuus
 2 years ago
Best ResponseYou've already chosen the best response.0i mean you can't have more pivot 'rows' than rows

s3a
 2 years ago
Best ResponseYou've already chosen the best response.0No, it cannot. I now get the answer to that subquestion.

s3a
 2 years ago
Best ResponseYou've already chosen the best response.0I mean my subquestion not part (b). Let me look at 3(b) again

s3a
 2 years ago
Best ResponseYou've already chosen the best response.0Also is dim N(A) = dim ("the x variable vector in Ax = 0")?

ingenuus
 2 years ago
Best ResponseYou've already chosen the best response.0i don't know whether you've heard the mit ocw lecture or not, but you should know dim N(A) = n r

ingenuus
 2 years ago
Best ResponseYou've already chosen the best response.0matrix is 3by 5 so n=5

s3a
 2 years ago
Best ResponseYou've already chosen the best response.0I haven't. Is N(A) = n  r something I am supposed to "just memorize"?

ingenuus
 2 years ago
Best ResponseYou've already chosen the best response.0well dim N(A) is number of vectors in basis of nullspace of A

ingenuus
 2 years ago
Best ResponseYou've already chosen the best response.0think about the basis of nullspace of A think how you get those bases

s3a
 2 years ago
Best ResponseYou've already chosen the best response.0(where n and r are of the matrix A) (Sorry for the potentially dumb question, I'm kind of braindead at the moment but, like I said, I cannot take a break.)

s3a
 2 years ago
Best ResponseYou've already chosen the best response.0(My break will be when I sleep.)

ingenuus
 2 years ago
Best ResponseYou've already chosen the best response.0can you think how you obtain the null space of A?

ingenuus
 2 years ago
Best ResponseYou've already chosen the best response.0then it is clear cut that dim N(A) = nr

s3a
 2 years ago
Best ResponseYou've already chosen the best response.0you find the vector x in Ax = 0

ingenuus
 2 years ago
Best ResponseYou've already chosen the best response.0yeah i'm asking do you know the exact procedures

s3a
 2 years ago
Best ResponseYou've already chosen the best response.0get A^(1) and multiply both sides?

s3a
 2 years ago
Best ResponseYou've already chosen the best response.0i mean left multiplication on each side of the equation

ingenuus
 2 years ago
Best ResponseYou've already chosen the best response.0since there are r pivot columns, there are nr free columns and there are nr special solutions to the null space. And they form basis for nullspace. so dim N(A)=nr

ingenuus
 2 years ago
Best ResponseYou've already chosen the best response.0you can do that only when a is invertible

ingenuus
 2 years ago
Best ResponseYou've already chosen the best response.0you use elimination process to compute nullspace right?

ingenuus
 2 years ago
Best ResponseYou've already chosen the best response.0why don't you solve some examples to get dimN(A)=nr i think you know the definitions

s3a
 2 years ago
Best ResponseYou've already chosen the best response.0when a is invertible, like you said. I'm not grasping something fundamental though: what is the nullspace of A? is it x in Ax = 0? In other words, what object's dimension is n  r?

ingenuus
 2 years ago
Best ResponseYou've already chosen the best response.0nullspace(A) is a subspace in R^n, which a vector in it satisfies Ax=0

ingenuus
 2 years ago
Best ResponseYou've already chosen the best response.0it is just whole solutions to Ax=0

ingenuus
 2 years ago
Best ResponseYou've already chosen the best response.0solutions form a subspace, so they are called null'space'

s3a
 2 years ago
Best ResponseYou've already chosen the best response.0ok so it's a dimension of a vector space in which a vector x makes Ax = 0?

ingenuus
 2 years ago
Best ResponseYou've already chosen the best response.0for example, when A is invertible, x is only 0 and the N(A)={0}

ingenuus
 2 years ago
Best ResponseYou've already chosen the best response.0no nullspace is just a name of subspace

ingenuus
 2 years ago
Best ResponseYou've already chosen the best response.0dim N(A) is what you are saying

s3a
 2 years ago
Best ResponseYou've already chosen the best response.0ya for two seconds, my brain was thinking about dim N(A).

s3a
 2 years ago
Best ResponseYou've already chosen the best response.0Will you be here in 1..75 hours?

ingenuus
 2 years ago
Best ResponseYou've already chosen the best response.0you need to carry on the elimination yourself to see dim N(A) = nr

s3a
 2 years ago
Best ResponseYou've already chosen the best response.0(If you keep writing, I will come back and read what you said.)

ingenuus
 2 years ago
Best ResponseYou've already chosen the best response.0i have a pdf about nullspace. do you want it?

ingenuus
 2 years ago
Best ResponseYou've already chosen the best response.0http://ocw.mit.edu/courses/mathematics/1806sclinearalgebrafall2011/axbandthefoursubspaces/solvingax0pivotvariablesspecialsolutions/ download the lecture summary for that lecture. it has the just the right information for you. good luck

s3a
 2 years ago
Best ResponseYou've already chosen the best response.0thanks and sry for leaving abruptbly
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