- #1
Sanglee
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Homework Statement
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 counter-example.
Homework Equations
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 counter-example 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?