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Show the given matrix is a vector space and find its dimension

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Let W be the set of all 2x2 matrices of the form [a -b]. Then under the usual matrix operations W is
[b -a]
1. Not a vector space
2. a vector space of dimension 1.
3. a vector space of dimension 2.
4. a vector space of dimension 3.
5. a vector space of dimension 4.

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The solution gives detailed steps on showing the given matrix is a vector space and then finding its dimension.

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