WeBWorK : MA322Denc Secure https/webworkas.ulyedu/webwork2 /MA322Denomme/Web Hom

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WeBWorK : MA322Denc Secure https/webworkas.ulyedu/webwork2 /MA322Denomme/Web Homew ::: Apps N Netflix Hulu w, myUK D canvas D Rent Electricity Water Time Previous Problem Problem List Next Problerm (1 point) Let V R2, let H be the subset of V of all points on the line y = 3x and let K be the subset of V of all points on the line y = 2x. Is HUK a subspace of the vector space V? 1. Is HUK nonempty? choose 2. Is HUK closed under addition? If it is, enter CLOSED. If it is not, enter two vectors in HUK whose sum is not in HUK using a comma separated list and syntax such as 1,2>, 3. Is HUK closed under scalar multiplication? If it is, enter CLOSED. If it is not, enter a scalar in R and a vector in HUK whose product is not in H U K, using a comma separated list and syntax such as 2, 41s H U K 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 Note: In order to get credit for this problem all answers must be correct Preview My Answers Submit Answers O Type here to search

Explanation / Answer

Answer (Q.1): since (o,o) belongs to HUK. So HUK is nonempty.

Answer (Q.2):(1,3), (1,2)

Answer (Q.3):CLOSED.

(Since H and K are closed under scalar multiplication,so it follows that,HUK is closed under scalar multiplication.

Answer (Q.4):No,HUK is not a subspace.(explanation : subspace must be closed under addition and scalar multiplication,but from above (Q.2),we see that,HUK is not closed under addition and hece it is not a subspace)

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