determine whether the given set is closed under the usual operations of addition and scalar multiplication, and is a (real) vector space.

The set of all 2 x 2 matrices of the form
[x 1]
[1 x]

where each x may be any scalar.

Question

determine whether the given set is closed under the usual operations of addition and scalar multiplication, and is a (real) vector space. 

The set of all 2 x 2 matrices of the form 
[x 1]
[1 x]

where each x may be any scalar.

anonymous · Answer

Remember the formula!

anonymous · Answer

I know i have to show that x+v=v for all vectors v, but im not quite sure how to go about doing it

anonymous · Answer

*and I also have to show that cu is in V but I'm not sure about how to go about it either =/

anonymous · Answer

ya you can !

anonymous · Answer

Go dude according to the CoC I have supported you and encouraged you rest... I believe you can do!

anonymous · Answer

well if you do a scalar multiplication on this, suppose with any constant c... so we'll get:
[cx c]
[c cx] 
the a_11 and a_22 entries are just a multiplication if a constant and a scalar hence it is also a scalar. But the a_12 and a_21 entries which are c and c are not 1 so this is not in the set so the set is not closed under scalar multiplication hence, not a  vector space.