What is the basis for the given subspace in R^5?

  • Thread starter Thread starter sallies
  • Start date Start date
  • Tags Tags
    Basis Subspace
sallies
Messages
1
Reaction score
0

Homework Statement



find a basis for the subspace R^5 that consists of all the vectors of the form [(b-c), (d-2b), (4d), (c-2d), (6d+2b)]

Homework Equations





The Attempt at a Solution



the only solution I can think of is e1, e2, e3, e4, e5... I don't think it's that simple though... would appreciate any input on this question. Thanks!
 
Physics news on Phys.org
Code: 
a = b - c
b = -2b   + d
c =         4d
d =      c - 2d
e = 2b     + 6d
A vector in this subspace is a linear combination of three vectors, which you can pick out of the equations above.
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
View full post »

Similar threads

Dimension and basis for a subspace
Replies
18
Views
2K
Find the basis of a vector subspace of R^2,2
Replies
9
Views
3K
Note that you can use the same c1, c2, and c3 for both parts.
Replies
2
Views
2K
Understanding Linear Algebra Subspaces and Matrices: A Homework Guide
Replies
18
Views
2K
Vector Subspace: Show S is a Subspace, Determine Basis & Find Dimension
Replies
2
Views
1K
Finding the basis of a subspace
Replies
6
Views
1K
Does W Qualify as a Subspace of R^3?
Replies
5
Views
2K
Finding a Basis for P2 Subspace with p'(5)=0
Replies
20
Views
3K
[Linear Algebra] Another question on subspaces
Replies
15
Views
2K
[Linear Alg] Determining which sets are subspaces of R[x]
Replies
7
Views
2K

Hot Threads

Recent Insights

Back
Top