Non homogeneous system question

  • Thread starter nhrock3
  • Start date
  • #1
415
0
there is a system Ax=b (x and b are vectors)
A is a system of kxn type
the system has at leas one solution:
1.
if k>n does the system has endless solutions
??
2.
if k=n and Ax=b has a single solution then for any system Ax=c has a solution
??


for 1:
i dont know why we need the other data k<n means we have free variables so its endless solutions

for 2:
i dont know whats c
 

Answers and Replies

  • #2
35,222
7,038
For 1, you are answering a different question than the one given.

For 2, if you are given that k = n and Ax = b has a unique solution, how would you find this solution? How would you find the solution to Ax = c?
 
Last edited:
  • #3
112
0
one of the ways i think about part 2 is that if Ax=b has a unique solution, then if we take the matrix A and augment it with b, then A can row reduce down to a nxn identity matrix. the augmented part depends on b, certainly, but if A reduces down, then b doesn't really matter, at least considering the row operations required to get the identity. So if we keep track of the row operations we performed on A to get the solution for b, we can perform those same row operations on just any vector c to get the appropriate solution.
 

Related Threads on Non homogeneous system question

  • Last Post
Replies
2
Views
3K
Replies
1
Views
1K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
1
Views
1K
Replies
5
Views
3K
Replies
0
Views
883
Replies
3
Views
3K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
2
Views
2K
Top