- #1
kdawghomie
- 3
- 0
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?