Question

How would you show 0 vector is in K if it is K= (X is in M, bx=xb)?

Answer 1

So \(K=\{x\in M|bx=xb\}\), where \(M\) is a vector space?

Answer 2

And \(b\) is just a fixed vector in \(M\)?

Answer 3

yes!

Answer 4

M is a subspace of a vector space actually..

Answer 5

Well, what is \(b*0\) and what is \(0*b\)?

Answer 6

can I just say that b is a 0 vector?

Answer 7

No. That's not a good way to do it. But what is \(b*0\)?

Answer 8

so just say that 0=0?

Answer 9

how is vector product defined?

Answer 10

That's something else I just recently noticed as well. Are these matrices?

Answer 11

yes!

Answer 12

So if you take any matrix and multiply it by the zero matrix, what do you get?

Answer 13

0

Answer 14

Right. So \(b*0=0\) and \(0*b=0\). So \(b*0=0*b\), and \(0\in K\).

Answer 15

okay I get it now, thanks

Answer 16

You're welcome.