My Math Forum  

Go Back   My Math Forum > College Math Forum > Linear Algebra

Linear Algebra Linear Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
December 22nd, 2018, 01:35 AM   #1
Newbie
 
Joined: Dec 2018
From: Tel Aviv

Posts: 4
Thanks: 0

Question 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 progressing… 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.
pregunto is offline  
 
January 11th, 2019, 07:36 AM   #2
Banned Camp
 
Joined: Mar 2015
From: New Jersey

Posts: 1,720
Thanks: 125

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.
zylo is offline  
Reply

  My Math Forum > College Math Forum > Linear Algebra

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 01:34 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 10:55 PM
the general solution of the recurrence relation Tiome_nguyen Calculus 2 May 23rd, 2012 09:45 PM
Closed-form solution of a recurrence relation. ChessTal Linear Algebra 5 July 4th, 2011 07:03 AM





Copyright © 2019 My Math Forum. All rights reserved.