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

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

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