# Basis of a vector space

karnten07

## Homework Statement

Determine whether the following 2 x 2 matrices form a basis of the vector space M2x2(R) of all (2x2)-matrices over R:

A1=
1 0
0 0

A2=
2 2
0 0

A3=
3 2
1 0

A4=
4 3
2 1

## The Attempt at a Solution

So for them to be bases, they must be a linearly independant set that spans the vector space. How can i go about showing this for each matrix?

Staff Emeritus
Gold Member
The question asked if those vectors form a basis. The question didn't ask if each individual vector was a basis (such a question wouldn't even make sense).

karnten07
The question asked if those vectors form a basis. The question didn't ask if each individual vector was a basis (such a question wouldn't even make sense).

Do i need to show that each matrix is invertible?

Staff Emeritus
Gold Member
I think you need to start with the definitions, to make sure you understand just what the question is asking.

karnten07
I think you need to start with the definitions, to make sure you understand just what the question is asking.

Oh so a1...a4 must all be linealry independant?

Staff Emeritus
Gold Member
Oh so a1...a4 must all be linealry independant?
Yes, that is what you need to show.

karnten07
Yes, that is what you need to show.

Thanks, library closes now and no internet at new flat

Homework Helper
Try to solve c1*A1+c2*A2+c3*A3+c4*A4=0. It's pretty easy. What are the solutions for c1...c4? What does that say about linear independence?

riordo
Hi, If I have a question i post it here and you will respond (if you are on line)?

riordo
Hi DIck can you help me with this problem..."find the determinant of the linear transformation T(M)=[1,2,2,3]M+M[1,2,2,3] from the space V of symmetric 2x2 matrices to V