Basis for 2x2 Matrix: Understand the Concepts

[math2010]

Homework Statement

What is a basis for the space of 2 x 2 matrices.

The Attempt at a Solution

I don't understand how to this at all. Is the 2x2 identity matrix abasis for 2x2 matrices? Because it's linearly independent and spanning the space? Can anyone explain?

 

[cronxeh]

Is the 2x2 identity matrix abasis for 2x2 matrices? Because it's linearly independent and spanning the space? Can anyone explain?

Yeap. Any 2x2 matrix in R^2 can be spanned by {(1,0),(0,1)} which is I2

 

[Mark44]

Homework Statement

What is a basis for the space of 2 x 2 matrices.

The Attempt at a Solution

I don't understand how to this at all. Is the 2x2 identity matrix abasis for 2x2 matrices? Because it's linearly independent and spanning the space? Can anyone explain?

I disagree with what Cronxeh said. The space of 2x2 matrices has dimension 4, so cannot be spanned by two vectors, let alone two vectors in R².

The standard basis for M_2,2 consists of these four matrices:
[1 0]
[0 0]

[0 1]
[0 0]

[0 0]
[1 0]

[0 0]
[0 1]