Reference no: EM131015005
1) Let V = R2, let H be the subset of V of all points on the line y = 3x, and let K be the subset of V of all points on the line y = -2x. Is H U K a subspace of the vector space V?
1. Does H U K contain the zero vector of V?
2. Is H U K 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 <1, 2>, <3, 4>.
3. Is H U K closed under scalar multiplication? If it is, enter CLOSED. If it is not, enter a scalar in R and a vector in H U K whose product is not in H U K, using a comma separated list and syntax such as 2, <3, 4>.
4. Is H U K a subspace of the vector space V? You should be able to justify your answer by writing a complete, coherent, and detailed proof based on your answers to parts 1-3.
2) Let V = R2, let H be the subset of V of all points on the line y = 3x, and let K be the subset of V of all points on the line y = x/3. Is H a subspace of the vector space V?
1. Does H U K contain the zero vector of V?
2. Is H U K 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 <1, 2>, <3, 4>.
3. Is H U K closed under scalar multiplication? If it is, enter CLOSED. If it is not, enter a scalar in R and a vector in H U K whose product is not in H U K, using a comma separated list and syntax such as 2, <3, 4>.
4. Is H U K a subspace of the vector space V? You should be able to justify your answer by writing a complete, coherent, and detailed proof based on your answers to parts 1-3.
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