1. ## Vector spaces-subspace

V= {B $\in M_{n}(R)$. B is skew symmetric.}

How can i show V is a subspace of $M_{n}(R)$?

2. Originally Posted by maths900
V= {B $\in M_{n}(R)$. B is skew symmetric.} How can i show V is a subspace of $M_{n}(R)$?
Do you know that $0 \in V$?
Can you show that $\left\{ {C,D} \right\} \subset V\;\& \;s \in \Re \; \Rightarrow \;C + sD \in V$?

3. Originally Posted by Plato
Do you know that $0 \in V$?
Can you show that $\left\{ {C,D} \right\} \subset V\;\& \;s \in \Re \; \Rightarrow \;C + sD \in V$?
Sorry can you explain what you have written. Thanks.

5. Originally Posted by Plato
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?

6. Originally Posted by maths900
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?

7. Lol yea of course, i understand that now.

How do i go about starting it? Shall i introduce a skew symmetric matrix/matrices??

8. Originally Posted by maths900
How do i go about starting it? Shall i introduce a skew symmetric matrix/matrices??
What do you know about skew symmetric matrix/matrices?

9. Originally Posted by Plato
What do you know about skew symmetric matrix/matrices?
B transposed = -B, is that correct?

10. Originally Posted by maths900
B transposed = -B, is that correct?
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?

11. Originally Posted by Plato
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.

12. Will its dimension be 2n or n^2?