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mathsforumhelp

Member

Registered: 2009-10-07

Posts: 14

Maths

You are given that A is an 5 x 9 matrix of nullity 5.
1.  The null space of A is a d-dimensional subspace of Rn, where
     d =______and n =_______
2.  The rank of A is______

3.  The row space of A is a d-dimensional subspace of Rn, where
     d =_______and n =________

4.  The column space of A is a d-dimensional subspace of Rn, where
     d =______and n =________   
5.  Are the row vectors of A linearly independent?
6.  Are the column vectors of A linearly independent?

7.  The number of parameters in the solution of ATx = 0 is__________
8.  For every b belongs to R9, the system ATx = b is consistent.

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Maths

It seems like you are posting your homework so others can do it for you.  Please show us what you're thinking thus far on the problem.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

mathsforumhelp

Member

Registered: 2009-10-07

Posts: 14

Re: Maths

I have managed to work out these answers please check that its right
1. d = 4 n = 9
2. 4
3. d = 5 n = 5