Hi, I understand what these two ideas mean, but I'm a bit lost on how to actually sit down and work out algebraically whether a set contains both properties or not.
An example to illustrate my point:
Determine whether the set of all 2x2 matrices whose determinant is 0 is a subspace of M22 (all 2x2 matrices).
My thinking went something like this
Matrix 1. AD-BC
Matrix 2. FG-HJ
hence if (A+F)(D+G)-(B+H)(C+J)=0 then the subset was close under vector addition. What is wrong with my thought train here?
For multiplication I figured something like
hence subset was closed under scalar multiplication, is this correct?
Thanks a heap in advance,