# Finding a basis for a subspace

#### ver_mathstats

Problem 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.

Related Calculus and Beyond Homework News on Phys.org

#### LCKurtz

Homework Helper
Gold Member
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.

#### WWGD

Gold Member
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).

"Finding a basis for a subspace"

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving