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-   -   Null space vs Col space dimension? (http://www.physicsforums.com/showthread.php?t=406463)

Shaybay92 May29-10 07:00 AM

Null space vs Col space dimension?
 
I have a question in my linear algebra text that asks:

Give integers p and q such that Nul A is a subspace of Rp and Col A is a subspace of Rq.



What determines these values? Why are the values of p and q different between the Nul space and Col space? The matrix in question is a 3 x 4 matrix and the value for Col A was 3 and Nul A was 4.

3 2 1 -5
-9 -4 1 7
9 2 -5 1


Why are they different? I would have thought the dimension was just the number of entires in each column. How can Nul space be 4 dimensions when there are only 3 entries in the column vectors?

Office_Shredder May29-10 07:05 AM

Re: Null space vs Col space dimension?
 
The null space is the kernel of the matrix. What is the domain of your matrix?

Shaybay92 May29-10 07:06 AM

Re: Null space vs Col space dimension?
 
What do you mean by kernel?


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