Null space vs Col space dimension?

  • Thread starter Shaybay92
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  • #1
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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?
 

Answers and Replies

  • #2
Office_Shredder
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The null space is the kernel of the matrix. What is the domain of your matrix?
 
  • #3
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What do you mean by kernel?
 

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