I have this question:
Show that the set of all $2 \times 2$ matrices with real coefficients forms a linear space over $\Bbb R$ of dimension $4$.
I know that the set of the matrices will basically form a linear combination which will define the vector space and they satisfy the axioms defined for the vector space.
I do not know how to show that this is possible. Do the vectors have to be linearly independent?
Any sort of help is appreciated.