Finding a basis for a subspace

  • #1
ver_mathstats
253
21
Homework Statement:
Find a basis for the subspace in R[SUP]4[/SUP] consisting of the form (a,b,c,d) when c=2a+2b and d=a-5b
Relevant Equations:
c=2a+2b and d=a-5b
I had assumed that we had to put our values into a matrix so I did [1 2 -1 0; 1 -5 0 -1] and then I would do a=[1; 1] and repeat for b, c, and d. This is incorrect however. I also thought that it could be {(1, 2, -1, 0),(1, -5, 0, -1)} however this was not the answer, and I am unsure of what do to next and hints would be appreciated.

Thank you.
 

Answers and Replies

  • #2
LCKurtz
Science Advisor
Homework Helper
Insights Author
Gold Member
9,568
774
I guess I would try this:$$
(a,b,c,d) = a(1,0,?,?) + b(0,1,?,?) $$
and fill in the ? spaces to make it work.
 
  • #3
WWGD
Science Advisor
Gold Member
6,291
8,174
One way that helps me make sense is to first determine the number of free variables in your subspace, i.e., variables that can take on any value. Then you choose to assign values by convenience to these (usually value 1, 0 are used/convenient).
 

Suggested for: Finding a basis for a subspace

Replies
4
Views
557
  • Last Post
Replies
7
Views
886
Replies
6
Views
1K
Replies
14
Views
606
Replies
10
Views
870
Replies
15
Views
860
  • Last Post
Replies
19
Views
934
  • Last Post
Replies
3
Views
522
Replies
2
Views
330
Top