both the questions. Which of the following sets are subspaces of R°?A. {(8,y, z) | y, z arbitrary numbers }B. {(x, y, z) | x, y, z > 0}C. {(-2x – 9y,–6x + 4y, 3x –MD. {(r, y, z) | x + y + z = 2}ME. {(x, y, z) | – 8x – 5y = 0, 7x – 2z = 0}F. {(x, y, z) | x + y+z= 0}4y) | x, y arbitrary numbers } Let H be the set of all points in the second and fourth quadrants in the plane V = R2. That is, H = {(x, y) | y <0}. Is H a subspaceof the vector space V?1. Does H contain the zero vector of V?choose2. 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 commaseparated 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 notin 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 detailedproof based on your answers to parts 1-3.choose

Name: both the questions. Which of the following sets are subspaces of R°?A.
Uploaded: 2024-03-20T06:38:44.000Z
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Description: both the questions. Which of the following sets are subspaces of R°?A. {(8,y, z) | y, z arbitrary numbers }B. {(x, y, z) | x, y, z > 0}C. {(-2x – 9y,–6x + 4y, 3x –MD. {(r, y, z) | x + y + z = 2}ME. {(x, y, z) | – 8x – 5y = 0, 7x – 2z = 0}F. {(x, y, z