(1 point) Let V = R³ and let H be the subset of V of all points on the plane 7x + 4y − 6z = 28. Is H a subspace of the v

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1 Point Let V R And Let H Be The Subset Of V Of All Points On The Plane 7x 4y 6z 28 Is H A Subspace Of The V 1 (31.93 KiB) Viewed 30 times

(1 point) Let V = R³ and let H be the subset of V of all points on the plane 7x + 4y − 6z = 28. Is H a subspace of the vector space V? 1. Does H contain the zero vector of V? H contains the zero vector of V 2. Is H closed under addition? If it is, enter CLOSED. If it is not, enter two vectors in HI whose sum is not in H, using a comma separated list and syntax such as <1,2,3>, <4,5,6>. <1,1,1>, <1,1,0> 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, <3,4,5>. CLOSED 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. H is a subspace of V