1 point) Let V R2, let H be the subset of V of all points on the line y --4x, an

Question

1 point) Let V R2, let H be the subset of V of all points on the line y --4x, and let K be the subset of V of all points on the line y = 3x. Is H u K a subspace of the vector space V? 1. Is H UK nonempty? choose 2. Is H UK closed under addition? If it is, enter CLOSED. If it is not, enter two vectors in H U K whose sum is not in H U K , using a comma separated list and syntax such as , . 3. ls H UK closed under scalar multiplication? If it is, enter CLOSED. If it is not, enter a scalar in R and a vector in HUK whose product is not in H U K, using a comma separated list and syntax such as 2, 4. Is H UK a subspace of the vector space V? You should be able to justify your answer using the subspace test (Theorem 4.5) and your answers to parts 1-3. choose

Explanation / Answer

(1,-4) +(1,3) = (2,-1)(1,-4) +(1,3) = (2,-1)

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