Checking Subspace: Problem Solution

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SUMMARY

The discussion focuses on verifying the properties of a subspace in linear algebra. The user is checking three conditions: the inclusion of the zero vector, closure under addition, and closure under scalar multiplication. It is concluded that the first condition is not satisfied, as the transformation A*[0 0]^t does not yield the expected result of [1 2]^t, indicating that the zero vector is not in the set S.

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Clandry
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Hi. I'm trying to check if my approach is right.

The problem is attached.

I need to check these:
1) 0 vector is in S
2) if U and V are in S then U+V is in S
3) if V is in S, then cV where c is a scalar is in S

The 1st condition is not satisfied right?
Since A*[0 0]^t=[0 0]^t≠[1 2]^t?
 

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Right.
 

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