(LinearAlgebra) all 2x2 invertible matrices closed under addition?by Sanglee Tags: addition, invertible, linearalgebra, matrices 

#1
Aug411, 12:41 AM

P: 6

1. The problem statement, all variables and given/known data
Suppose V is a vector space. Is the set of all 2x2 invertible matrices closed under addition? If so, please prove it. If not, please provide a counterexample. 2. Relevant equations 3. The attempt at a solution well i know that what does it mean to be closed under addition. When V is closed under addition, if I suppose vector u and w are in the V, their addition u+w is also in the V, right? The answer for the question is No. A counterexample my professor provided is I+(I)=0 I and (I) are invertible, but their addition 0 is not invertible. and I know why it's not invertible. But I don't figure out why it is not closed under addition,,. If the addition is not invertible, does it mean that the addition is not in the V? 



#2
Aug411, 02:22 AM

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Thanks
PF Gold
P: 11,521





#3
Aug411, 03:53 AM

P: 6

So clear, easy to understand. Thanks!



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