anonymous
  • anonymous
1) Consider the following attempt to define a vector space that does not work. Let V be the set R2 with the standard vector addition and an unusual scalar multiplication defined by (a, b) + (c, d) = (a + c, b + d) k ๏(a, b) = (k 2a, k 2b) . (The funny symbol for scalar multiplication is meant to emphasize that it’s not the standard definition.) It turns out that all axioms hold except for axiom #8. a) Prove that axiom #9 holds for any scalars k and m and any vector (a, b) . b) Show that axiom #8 does not hold in general by finding particular scalars k and m and a particular vector (a, b) that
Mathematics
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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anonymous
  • anonymous
1) Consider the following attempt to define a vector space that does not work. Let V be the set R2 with the standard vector addition and an unusual scalar multiplication defined by (a, b) + (c, d) = (a + c, b + d) k ๏(a, b) = (k 2a, k 2b) . (The funny symbol for scalar multiplication is meant to emphasize that it’s not the standard definition.) It turns out that all axioms hold except for axiom #8. a) Prove that axiom #9 holds for any scalars k and m and any vector (a, b) . b) Show that axiom #8 does not hold in general by finding particular scalars k and m and a particular vector (a, b) that
Mathematics
katieb
  • katieb
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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