Question

For each given set, addition operation, scalar multiplication determine whether the group is a vector space over the reals.

The set of all 2x2 lower triangle matrices with normal addition and scalar multiplication.

show work for all properties:

1. closure property of addition

2. communitive property of addition

3. Associative property of addition

4. additive identity element

5. additive inverse property

6. closure property of scalar multiplication

7. distributive property of scalor over vectors

8. distributive propert of scalars over a vector

9. associative property of scalar multiplication

10. scalar multiplication identity element