V= {B $\displaystyle \in M_{n}(R)$. B is skew symmetric.} How can i show V is a subspace of $\displaystyle M_{n}(R)$?
Do you know that $\displaystyle 0 \in V$?
Can you show that $\displaystyle \left\{ {C,D} \right\} \subset V\;\& \;s \in \Re \; \Rightarrow \;C + sD \in V$?
Do you know that $\displaystyle 0 \in V$?
Can you show that $\displaystyle \left\{ {C,D} \right\} \subset V\;\& \;s \in \Re \; \Rightarrow \;C + sD \in V$?
Sorry can you explain what you have written. Thanks.
What about my answer do you not understand?
What does your textbook say about subspaces of vector spaces?
All of it
My lecture notes show that for it to be a subspace it has to satisfy three axioms.
I know that 0 belongs to V, but how would i apply that to skew symmetric matrices?
All of it
My lecture notes show that for it to be a subspace it has to satisfy three axioms.
I know that 0 belongs to V, but how would i apply that to skew symmetric matrices?
Is the sum of two of skew symmetric matrices a skew symmetric matrix?
If you multiply a skew symmetric matrix by a real number do you get a symmetric matrix?
Yes. Now answer the two question.
Is the sum of two of skew symmetric matrices a skew symmetric matrix?
If you multiply a skew symmetric matrix by a real number do you get a symmetric matrix?
Yes. Now answer the two question.
Is the sum of two of skew symmetric matrices a skew symmetric matrix?
If you multiply a skew symmetric matrix by a real number do you get a symmetric matrix?
Yes i do
How can I show V is not an empty set....1st axiom
EDIT: Lol its pretty obvious now. I just have to write down any skew symmetric matric i guess. Thanks. You made it sound much easier.
Last edited by maths900; Feb 17th 2009 at 09:50 AM.