SOLUTION: Could you help me on how to do part b) and if I am correct in the other sections? Let V=R2, let H be the subset of V of all points on the line y=−4x, and let K be the subset o

Question 1177515: Could you help me on how to do part b) and if I am correct in the other sections?
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∪K a subspace of the vector space V?
a)Does H∪K contain the zero vector of V? Answer:H union K contains the zero vector og V
b)Is H∪K closed under addition? If it is, enter CLOSED. If it is not, enter two vectors in H∪K whose sum is not in H∪K, using a comma separated list and syntax such as <1,2>, <3,4>.
Answer:
c)Is H∪K closed under scalar multiplication? If it is, enter CLOSED. If it is not, enter a scalar in R and a vector in H∪K whose product is not in H∪K, using a comma separated list and syntax such as 2, <3,4>.
Answer:Closed
d)Is H∪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.
Answer: H union K is not a subspace of V.

Answer by Solver92311(821) (Show Source): You can put this solution on YOUR website!

There is only one vector in the union of H and K, namely <0,0>

John

My calculator said it, I believe it, that settles it

From
I > Ø

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