How can I determine if a set of vectors forms a subspace?

  • Thread starter Thread starter phy
  • Start date Start date
  • Tags Tags
    Subspace Vector
AI Thread Summary
To determine if a set of vectors forms a subspace, one must check if linear combinations of the vectors can generate all elements in the target space. The discussion revolves around using the equation e*A + f*B + g*C to express a matrix with specific entries. The term VecR(A, B, C) is suggested to refer to a spanning set, although its notation is not commonly found in linear algebra textbooks. The solution approach involves setting the linear combination equal to the target matrix and solving for the coefficients. The expected outcome is a proportional relationship rather than a specific numerical solution.
phy
Hi guys. I need some help with question #5 from my assignment. If someone can just tell me how to get the question started, it would be great. Thanks :smile:

http://img34.exs.cx/img34/8320/algebra1.jpg
 
Physics news on Phys.org
If A, B and C generate U then e*A +f*B + g*C generates every element in U (in this case that a b c d matrix). Of course you know this already seeing as you did the rest of those. What does VecR(A, B, C) mean? No linear alg. book I've ever worked with uses that notation.
 
I'm not 100% sure on this either but somebody who I spoke to said that VecR(A, B, C) is just a spanning set. I couldn't find it in my textbook either.

So would I just set e*A +f*B + g*C equal to the matrix with entries a b c d and then solve?
 
phy said:
I'm not 100% sure on this either but somebody who I spoke to said that VecR(A, B, C) is just a spanning set. I couldn't find it in my textbook either.

So would I just set e*A +f*B + g*C equal to the matrix with entries a b c d and then solve?

Ok that's what I figured. Yeah and you should get some sort of proportionality between the four and not a numerical answer once you solve it out.
 
Alrightie I'll do that. Thanks a lot =)
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

I Vector subspace and basis vectors in the context of data science
Replies
6
Views
3K
Suvat vector versus the scalar form
Replies
44
Views
4K
What Are Vector Subspaces in Linear Algebra?
Replies
2
Views
3K
Help with linear algebra: vectorspace and subspace
Replies
15
Views
3K
I Pseudo-Riemaniann isometries
Replies
4
Views
1K
I Showing that a set of differentiable functions is a subspace of R
Replies
19
Views
5K
MHB Can These Mathematical Sets Be Considered Subspaces?
Replies
1
Views
1K
I Does a set and a field together always generate a vector space?
Replies
28
Views
3K
Syntax Error? x and y components of E field in unit vector form
Replies
13
Views
2K
Stuck on a few Vector homework problems
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top