Let V = R'and let H be the subset of V of all points on the plane 5r + 2y + 7z = 10. Is Ha subspace of the vector space V? 1. Is H nonempty? His empty 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>, <4,5,6>. <2,0,0 >,<0,5,0 > 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, <3,4,5>. 2, <2,0,0 > 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. H is a subspace of V Note: In order to get credit for this problem all answers must be correct.
Let V = R'and let H be the subset of V of all points on the plane 5r + 2y + 7z = 10. Is Ha subspace of the vector space V? 1. Is H nonempty? His empty 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>, <4,5,6>. <2,0,0 >,<0,5,0 > 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, <3,4,5>. 2, <2,0,0 > 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. H is a subspace of V Note: In order to get credit for this problem all answers must be correct.
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 V = Rand let H be the subset of V of all points on the plane 5x + 2y+ 7z = 10. Is H a subspace of the vector space V?
1. Is H nonempty?
His empty
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>, <4,5,6>.
<2,0,0 >,<0,5,0>
3. Is H closed under scalar multiplication? If it is, enter CLOSED. If it is not, enter a scalar in Rand a vector in H whose product is not in H, using a
comma separated list and syntax such as 2, <3,4,5>.
2, < 2,0,0 >
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.
H is a subspace of V
Note: In order to get credit for this problem all answers must be correct.
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