Verify your answer with theappropriate calculations

1. [8 points] Let y be the set of all positive real numbers. Let the operations of addition and scalar multiplication be dened as follows: 11 +I2 =3..le [:11 = If Determine if V, along with the dened operations forms a vector space. 1I.r'erify your answer with the appropriate calculations. 2. [4 points] Let'u' be the vector space of all 3 K 2 matrices. Let w be the set of all 3 In: 2 matrices ofthe form a b (a + 3b c ). Determine if W is a subspace of V. 1Iu|'erify your answer with appropriate calculations. a! r: + 5d 3. [4 points] Let 'u' be the vector space R3. Let W be the set of all ordered triples of the form (a, h, c) where a. = b2 + :2. Determine if W is a subspace of y. Verify your answer with appropriate calculations. 4. [2 points] Express [21 i] as a linear combination of [3 :11] ,[2 g] . [i 1143 i] if possible. If it is not possible, explain why. 5. [2 points] Express 172 3x + 2 as a linear combination of I 3. 2x + 1, and 5x 4 if possible. If it is not possible, explain why