Proving R^2*2 is a Vector Space: A Matrix Proof with Real Entries

[rygza]

show that the set of all 2x2 matrices with real entries, R^2*2 (that's a "double R"), is a vector space.

I have no clue how to approach this. The only thing i know is the standard basis for 2x2 matrices.

 

[LCKurtz]

Do you know how to add matrices? How to multiply them by a constant? Is there a 0 element? Do you know the list of properties that define a vector space?

 

[rygza]

Do you know how to add matrices? How to multiply them by a constant? Is there a 0 element? Do you know the list of properties that define a vector space?

I'm looking at my notes. My teacher skipped this part to try to dumb down the section for the class, but yea i see a list of 10 properties

 

[retspool]

I took Linear Algebra 2 last quarter.

I think you need to take the standard 2 x 2 matrix with the terms a,b,c,d belonging to R as matrix A and another matrix B with the terms e,f,g,h belonging to R

and then you need to use them in the 10 or the 8 axioms for vector spaces

hope it helps

 

[rygza]

I took Linear Algebra 2 last quarter.

I think you need to take the standard 2 x 2 matrix with the terms a,b,c,d belonging to R as matrix A and another matrix B with the terms e,f,g,h belonging to R

and then you need to use them in the 10 or the 8 axioms for vector spaces

hope it helps

THANK YOU!
yea the problem is this class is a mix of linear algebra and differential equations. It switches back and forth between the two, it can get tough for me

 

[retspool]

My bro took a joint course of L.A and Diff. Eq

He had a hard time, i took Diff eq. and L.A separately and i breezed away with it.