H be the set of all points in the fourth quadrant in the plane V = R². That is, H = {(x, y) | a> 0, y<0}. Is H a subspace of the ctor space V? 1. Does H contain the zero vector of V? choose 2. 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>. 3. 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>. 4. Is Ha 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. choose
H be the set of all points in the fourth quadrant in the plane V = R². That is, H = {(x, y) | a> 0, y<0}. Is H a subspace of the ctor space V? 1. Does H contain the zero vector of V? choose 2. 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>. 3. 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>. 4. Is Ha 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. choose
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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both the questions

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?
1. Does H contain the zero vector of V?
choose
2. 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>.
3. 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>.
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.
choose

Transcribed Image Text:Let V = R and let H be the subset of V of all points on the line 3x + 4y = 12. Is H a subspace of the vector space V?
1. Is H nonempty?
choose
2. 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>.
3. Is H closed under scalar multiplication? If it is, enter CLOSED. If it is not, enter a scalar in IR and a vector in H whose product is
not in H, using a comma separated list and syntax such as 2, <3,4>.
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.
choose
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