Vector spaces and matrices question

[sheelbe999]

Massively stuck with this one, have done some reading and am having difficulty connecting matrices to vector spaces

(a) Verify that the space of the real (2 x 2)-matrices, endowed with the standard addition
and multiplication by real scalars, forms a vector space
(b) Specify a basis for this vector space
(c) What is its dimension?

any help would be greatly appreciated.

 

[VeeEight]

For (a), you must show that the properties of a vector space are satisfied. See: http://en.wikipedia.org/wiki/Vector_space#Definition

For (b), find a set that spans this vector space (ie any vector in the space can be written as a linear combination of vectors in your spanning set). After you have done this, try to find the minimal number of vectors that can accomplish this. See: spanning set, linear independence

For (c), The dimension of the vector space is the number of vectors in the basis.