# Linear Algebra question: finding bases

## Homework Statement

The problem states:

Let

A_1 = [-1 1] , A_2 = [1 3]
.........[0 1]............[-1 0]

A_3 = [1 0] , A_4 = [0 -1]
.........[1 2]............[2 3]

Show that {A_1, A_2, A_3, A_4} is a basis for M_2 R.

The attempt at a solution

I'm very confused about this problem. I understand that to show {A_1, ..., A_4} is a basis, I must show 1.) the set is linearly independent, and 2.) it is a spanning set; however, I know there is a less complicated way instead of going through these 2 steps. I'm really not sure what the "easy" way is for doing this problem... it hints that there is a Thm that will help solve the problem, but I have found none that fit the bill. Can someone please help me with all this?

HallsofIvy