
Linear Algebra Linear Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
December 22nd, 2018, 02:35 AM  #1 
Newbie Joined: Dec 2018 From: Tel Aviv Posts: 4 Thanks: 0  Matrix in relation to solution subspace
Hi guys, I am having serious trouble analysing the following question: I have been thinking about it for an hour, but I am not progressingâ€¦ Can anybody help out? Let A be a matrix over R of order 4x4, with rank 2. Suppose that the vectors u=(2,1,2,0) v=(1,1,2,4) w=(1,0,2,1) are solutions to the linear system Ax=b. a. find the dimension of the solution space of the system Ax=0 and find its basis. b. find the general solution to the system Ax=b. 
January 11th, 2019, 08:36 AM  #2 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,641 Thanks: 119 
If A has rank 2 it will have 2 linear independent cols, a basis, which span the solution space, of dim 2. Ax=b has a solution for any b in the solution space.


Tags 
basis, dimension, matrix, relation, solution, solution subspace, subspace 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Question regarding Particular solution in recurrence relation  shanytc  Computer Science  4  May 30th, 2017 02:34 PM 
There's a Relation between 3 columns or rows of this matrix but it is very difficult  ormara  Linear Algebra  1  December 27th, 2014 11:55 PM 
the general solution of the recurrence relation  Tiome_nguyen  Calculus  2  May 23rd, 2012 10:45 PM 
Closedform solution of a recurrence relation.  ChessTal  Linear Algebra  5  July 4th, 2011 08:03 AM 