# Vector Spaces

## Homework Statement

Determine if the following sets are vector spaces

Part A) R^2; u+v = (u1 + v1, u2 + v2); cu = (cu1,cu2)

part b) M_2,2

A + B = |(a_11 + b_11) (a_12 + b_12)| & cA = |ca_11 ca_12|
|(a_21 + b_21) (a_22 + b_22)| |ca_21 ca_22|

sorry this is a little crude but those are both suppose to be 2X2 matricies

## The Attempt at a Solution

Part A) Yes, it is a vector space because it follows the addition & multiplication properties of vector spaces

Part B) yes it is a vector space because the set is closed under matrix addition & sclar multiplication

Are these statments true and a sufficient answer