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 one year 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?
 one year 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
 one year 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
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.0yes m=#rows n=#columns r=rank

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

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

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

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

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

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

s3a
 one year ago
Best ResponseYou've already chosen the best response.0Why is dim N(A) = nr=5r?

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

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

s3a
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.0well dim N(A) is number of vectors in basis of nullspace of A

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

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

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

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

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

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

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

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

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

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

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

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

s3a
 one year 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
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.0no nullspace is just a name of subspace

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

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

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

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

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

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

ingenuus
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.0thanks and sry for leaving abruptbly
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