Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
Find a basis for the space V of all skewsymmetric 3x3 matrices. What is the dimension of V?
 one year ago
 one year ago
Find a basis for the space V of all skewsymmetric 3x3 matrices. What is the dimension of V?
 one year ago
 one year ago

This Question is Closed

brinetheryBest ResponseYou've already chosen the best response.0
I'll be back in a sec. Brewing some coffee. Would you like some?
 one year ago

NodataBest ResponseYou've already chosen the best response.2
Yeah, I will in maybe two hours =P
 one year ago

NodataBest ResponseYou've already chosen the best response.2
Well you need to remember that a basis for any vectorial space generates it and it's vectors are linear independent.
 one year ago

NodataBest ResponseYou've already chosen the best response.2
And 3x3 skewsymmetric matrix is something like this:
 one year ago

NodataBest ResponseYou've already chosen the best response.2
Do you have any idea to begin with?
 one year ago

NodataBest ResponseYou've already chosen the best response.2
Mm you need three matrices am I right?
 one year ago

NodataBest ResponseYou've already chosen the best response.2
Well the dimension is 3 haha
 one year ago

brinetheryBest ResponseYou've already chosen the best response.0
and I need a longer explanation b/c A=A^T isn't gonna cut it
 one year ago

NodataBest ResponseYou've already chosen the best response.2
uff I almost burn my brain hehe
 one year ago

brinetheryBest ResponseYou've already chosen the best response.0
I told you linear algebra's no good!
 one year ago

NodataBest ResponseYou've already chosen the best response.2
Well I think that the three vectors are \[\left[\begin{matrix}0 & 1 & 0\\ 1 & 0 & 0\\ 0 & 0 & 0\end{matrix}\right]\]
 one year ago

NodataBest ResponseYou've already chosen the best response.2
Is the idea of a basis clear to you?
 one year ago

NodataBest ResponseYou've already chosen the best response.2
Like you know why (1,0,0), (0,1,0),(0,0,1) is the basis of R^3?
 one year ago

NodataBest ResponseYou've already chosen the best response.2
Well then you know that the basic idea behind a basis is that you can get any vector of the space by forming a linear combination.
 one year ago

NodataBest ResponseYou've already chosen the best response.2
like \[\vec{v}=a\hat{i} + b\hat{j} + c\hat{k}\]
 one year ago

NodataBest ResponseYou've already chosen the best response.2
well that is the idea in a graphic form.
 one year ago

NodataBest ResponseYou've already chosen the best response.2
If you want to obtain a basis for the 3x3 skew symmet
 one year ago

NodataBest ResponseYou've already chosen the best response.2
ric matrices you need to know that is the general form of matrix of that kind.
 one year ago

brinetheryBest ResponseYou've already chosen the best response.0
okay, I'm following what you're saying
 one year ago

NodataBest ResponseYou've already chosen the best response.2
the definition says that the elements of an skew symmetric matrix are such as: \[a_{ij}=a_{ji}\]
 one year ago

NodataBest ResponseYou've already chosen the best response.2
It seems that that doesn't tell us a lot about those matrices, but you can figure out what you have on the diagonal.
 one year ago

NodataBest ResponseYou've already chosen the best response.2
if i = j, then \[a_{ii}=a_{ji}\]
 one year ago

NodataBest ResponseYou've already chosen the best response.2
which is true if the diagonal is made up zeros.
 one year ago

NodataBest ResponseYou've already chosen the best response.2
and I think that's all. An 3x3 skew symmetrical matrix has this form:
 one year ago

brinetheryBest ResponseYou've already chosen the best response.0
Here's something... http://www.euclideanspace.com/maths/algebra/matrix/functions/skew/index.htm
 one year ago

NodataBest ResponseYou've already chosen the best response.2
\[\left[\begin{matrix}0 & a_{12} & a_{13} \\ a_{12} & 0 & a_{23}\\ a_{13} & a_{23} & a_{33} \end{matrix}\right]\]
 one year ago

brinetheryBest ResponseYou've already chosen the best response.0
Looks like it's all zeros down the diagonal.
 one year ago

brinetheryBest ResponseYou've already chosen the best response.0
you're a bad math teacher haha! :p
 one year ago

NodataBest ResponseYou've already chosen the best response.2
well now you can split that matrix on three parts:
 one year ago

brinetheryBest ResponseYou've already chosen the best response.0
Yep this part is where I need explaining...
 one year ago

NodataBest ResponseYou've already chosen the best response.2
\left[\begin{matrix}0 & a_{12} & 0 & \\ a_{12} & 0 & 0\\ 0&0&0\end{matrix}\right]
 one year ago

NodataBest ResponseYou've already chosen the best response.2
\[\left[\begin{matrix}0 & 0 & a_{13} & \\ 0 & 0 & 0\\ a_{13}&0&0\end{matrix}\right]\]
 one year ago

NodataBest ResponseYou've already chosen the best response.2
\[\left[\begin{matrix}0 & 0 & 0 & \\ 0 & 0 & a_{23}\\ 0&a_{23}&0\end{matrix}\right]\]
 one year ago

NodataBest ResponseYou've already chosen the best response.2
Is it clear why I did that?
 one year ago

brinetheryBest ResponseYou've already chosen the best response.0
Oh I see. So each part of the basis will be a 3x3 matrix?
 one year ago

brinetheryBest ResponseYou've already chosen the best response.0
And there will be (3) 3x3 matrices
 one year ago

NodataBest ResponseYou've already chosen the best response.2
yeah! it has to bee a 3x3 matrix
 one year ago

brinetheryBest ResponseYou've already chosen the best response.0
I asked on cramster and some (puta) was really insulting to me AND she gave me the wrong answer.
 one year ago

NodataBest ResponseYou've already chosen the best response.2
what is cramster? and puta?
 one year ago

NodataBest ResponseYou've already chosen the best response.2
we are not finished yet.
 one year ago

brinetheryBest ResponseYou've already chosen the best response.0
I thought it meant b)it(ch but I guess it's mexican slang for prostitute or whore
 one year ago

brinetheryBest ResponseYou've already chosen the best response.0
but you get the idea.
 one year ago

NodataBest ResponseYou've already chosen the best response.2
\[\left[\begin{matrix}0& 1 & 0 \\ 1 & 0 &0\\ 0&0&0\end{matrix}\right]\]
 one year ago

NodataBest ResponseYou've already chosen the best response.2
ahh I thought I did haha.
 one year ago

NodataBest ResponseYou've already chosen the best response.2
\[\left[\begin{matrix}0& 0 & 1 \\ 0 & 0 &0\\ 1&0&0\end{matrix}\right]\]
 one year ago

NodataBest ResponseYou've already chosen the best response.2
and \left[\begin{matrix}0& 0 & 0 \\ 0 & 0 &1\\ 0&1&0\end{matrix}\right]
 one year ago

NodataBest ResponseYou've already chosen the best response.2
You multiply by the scalars a,b,c each of those matrices and form a linear combination.
 one year ago

NodataBest ResponseYou've already chosen the best response.2
and the result is a skew symmetrical matrix
 one year ago

NodataBest ResponseYou've already chosen the best response.2
I'm sorry If my explanation was awful, and my english worst =P
 one year ago

brinetheryBest ResponseYou've already chosen the best response.0
So the dimension of all skewsymmetric matrices is 2?
 one year ago

brinetheryBest ResponseYou've already chosen the best response.0
or that's only the dimension of the basis?
 one year ago

NodataBest ResponseYou've already chosen the best response.2
the dimesion is the number of vectors of the basis. so it's 3.
 one year ago

brinetheryBest ResponseYou've already chosen the best response.0
hahaha I am so stupid!
 one year ago

brinetheryBest ResponseYou've already chosen the best response.0
WOW. I can't believe I asked that.
 one year ago

NodataBest ResponseYou've already chosen the best response.2
if you have an 4x4 skew symmetrical matrix the dimension of the basis is 4.
 one year ago

NodataBest ResponseYou've already chosen the best response.2
Don't worry, don't judge yourself so severely.
 one year ago

NodataBest ResponseYou've already chosen the best response.2
Do you have any doubt regarding this brinethery?
 one year ago

brinetheryBest ResponseYou've already chosen the best response.0
I have another question for you! No I don't have any doubt. You did a great job explaining.
 one year ago
See more questions >>>
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.