What is the dimension of M(2x2) over K? Find basis? (linear algebra)

M(2x2)(R) is a vector space of K.

M =

(a......b)

(-b.....a)

Re: What is the dimension of M(2x2) over K? Find basis? (linear algebra)

one way of thinking of a basis is it tells us: "how many pieces of information we need to specify". how many numbers (scalars) do you have to know to completely determine the matrix:

$\displaystyle \begin{bmatrix}a&b\\-b&a \end{bmatrix}$?

can you write the matrix as:

a*something + b*(another something)?

what might the "somethings" be?