Math Is Fun Forum

mathsforumhelp

Member

Registered: 2009-10-07

Posts: 14

Basis of row space column space

Let A be the matrix
3 2 2 -3
-6 -6 -7 3
-12 0 4 26
-9 -10 -12 -3
You are asked to find bases for the row and column spaces of A, and to answer a few other questions related to the rank and nullity of A.
1. A basis for the row space of A is
Are the row vectors of A linearly independent?
The rank of A is  and the nullity of A is___________
2.  Is the row space of A equal to R4?
Does the system Ax = 0 have only the trivial solution?
Is the matrix A invertible?
3. A basis for the column space of A is__________________
Are the column vectors of A linearly independent?
The rank of AT is  and the nullity of AT is____________________
4.Is the column space of A equal to R4?
Does the system ATx = 0 have only the trivial solution?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Basis of row space column space

Hi mathsforumhelp;

Over here I answered some similar type questions and showed a method to answer more of them.

http://www.mathisfunforum.com/viewtopic … 74#p121074

Did you see this reply? You did not answer so it is impossible for us to gauge your progress.  The only way to understand math is to do it. Please look at that post and see what you understand, or where I am not clear. Also, there is a page provided that covers all of this. Please give it a try.

If you work with us much of the type of linear algebra you are doing will be covered.

Last edited by bobbym (2009-10-09 12:15:03)

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If it ain't broke, fix it until it is.
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