Is M2 a Vector Space with Modified Scalar Multiplication?

[blazelian]

Is this a vector space?

Let M2 denote the set of all matrices of 2 x 2. Determine if M2 is a vector space when considered with the standard addition of vectors, but with scalar multiplication given by
α*(a b) = (αa b)
(c d) (c αd)
In case M2 fails to be a vector space with these definitions, list at least one axiom that fails to hold. justify you answer.

How do you solve this?

 

[pongo38]

Start with a good formal definition of a vector space.

 

[blazelian]

well a vector space is something tht looks like R^n

 

[Mark44]

well a vector space is something tht looks like R^n

That's not a formal definition. Your text should have a definition of a vector space, including about 10 axioms.