Vector spaces-subspace

**maths900** · February 17th 2009, 08:24 AM

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

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

**Plato** · February 17th 2009, 08:44 AM

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 $\left\{ {C,D} \right\} \subset V\;\& \;s \in \Re \; \Rightarrow \;C + sD \in V$ ?

**maths900** · February 17th 2009, 08:49 AM

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.

**Plato** · February 17th 2009, 08:57 AM

What about my answer do you not understand?
What does your textbook say about subspaces of vector spaces?

**maths900** · February 17th 2009, 09:01 AM

Originally Posted by Plato

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?

**Plato** · February 17th 2009, 09:07 AM

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?

**maths900** · February 17th 2009, 09:13 AM

Lol yea of course, i understand that now.

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

**Plato** · February 17th 2009, 09:16 AM

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?

**maths900** · February 17th 2009, 09:19 AM

Originally Posted by Plato

What do you know about skew symmetric matrix/matrices?

B transposed = -B, is that correct?

**Plato** · February 17th 2009, 09:25 AM

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?

**maths900** · February 17th 2009, 09:33 AM

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.

**maths900** · February 17th 2009, 09:58 AM

Will its dimension be 2n or n^2?

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