(. Let H be the set of all points in the fourth quadrant in the plane V = R². That is, H = {(x, y) | x > 0, y < 0}. Is H a subspace of the vector space V? Is H nonempty? choose Is H closed under addition? If it is, enter CLOSED. If it is not, enter two vectors in H whose sum is not in H, using a comma separated list and syntax such as <1,2>, <3,4>. Is H closed under scalar multiplication? If it is, enter CLOSED. If it is not, enter a scalar in R and a vector in H whose product is not in H, using a comma separated list and syntax such as 2, <3,4>. Is H 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.
(. Let H be the set of all points in the fourth quadrant in the plane V = R². That is, H = {(x, y) | x > 0, y < 0}. Is H a subspace of the vector space V? Is H nonempty? choose Is H closed under addition? If it is, enter CLOSED. If it is not, enter two vectors in H whose sum is not in H, using a comma separated list and syntax such as <1,2>, <3,4>. Is H closed under scalar multiplication? If it is, enter CLOSED. If it is not, enter a scalar in R and a vector in H whose product is not in H, using a comma separated list and syntax such as 2, <3,4>. Is H 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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:(.
Let H be the set of all points in the fourth quadrant in the plane V = R?. That is, H = {(x, y) | x > 0, y <0}. Is H a
subspace of the vector space V?
Is H nonempty?
choose
Is H closed under addition? If it is, enter CLOSED. If it is not, enter two vectors in H whose sum is not in H, using a
comma separated list and syntax such as <1,2>, <3,4>.
Is H closed under scalar multiplication? If it is, enter CLOSED. If it is not, enter a scalar in R and a vector in H whose
product is not in H, using a comma separated list and syntax such as 2, <3,4>.
Is H 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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