A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 4 years ago
A set of vectors form a basis for vector space V if the set of vectors are lin independent AND span V. So after finding the span of V you can simply find the basis by taking away lin dependent vectors right?
anonymous
 4 years ago
A set of vectors form a basis for vector space V if the set of vectors are lin independent AND span V. So after finding the span of V you can simply find the basis by taking away lin dependent vectors right?

This Question is Closed

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1a basis is the most efficient span. a span can contain useless vectors in it; for example, take a plane. a plane only need to be defined by 2 independant vectors. If you have a span that contains more than 2 vectors that are coplanar, then the extra vectors are useless in defining a basis.

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1\[span\begin{pmatrix}1&0&3\\0&1&2\end{pmatrix}\]is not a basis even tho it spans R^2. The column vector [3,2] can be formed from the first 2 and therefore provides no extra benefit in determing any other vector in the vectorspace.

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1To find the basis of a given matrix A; row reduce it to B and remove all the columns in A that relate to "free variables". The rest of the column vectors of A will form a basis.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.