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Mindscrape
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I am supposed to determine whether or not the following two sets constitute a vector space.
1) The set of all polynomials degree two.
2) The set of all diagonal 2 x 2 matrices.
For the first one, it will not be a vector space because it does not satisfy the closure property. Also the distributive property would be broken because a(x+y)^2 would not be (ax+ay)^2, or did I do that wrong?
The second one would not satisfy additivity properties, and not be a vector space.
Right? I don't know the set notation in LaTeX, so I'm not really sure how to put up much of my work.
1) The set of all polynomials degree two.
2) The set of all diagonal 2 x 2 matrices.
For the first one, it will not be a vector space because it does not satisfy the closure property. Also the distributive property would be broken because a(x+y)^2 would not be (ax+ay)^2, or did I do that wrong?
The second one would not satisfy additivity properties, and not be a vector space.
Right? I don't know the set notation in LaTeX, so I'm not really sure how to put up much of my work.