MA527_HW02_2023_Fall_Mossing_GRADED

MA52700 distance Homework 2 Joseph Mossing TOTAL POINTS 45 / 45 QUESTION 1 1 287 5 5 / 5 ✓ + 5 pts Correct + 4 pts small mistake + 3 pts mistake + 2 pts several mistakes + 1 pts something is right QUESTION 2 2 287 7 5 / 5 ✓ + 5 pts Correct + 4 pts small mistake + 3 pts mistake + 2 pts several mistakes + 1 pts something is right + 0 pts Did not solve the problem. QUESTION 3 3 300 12 5 / 5 ✓ + 5 pts Correct + 4 pts small mistake + 3 pts mistake + 2 pts several mistakes + 1 pts something is right QUESTION 4 4 300 22 5 / 5 ✓ + 5 pts Correct + 4 pts small mistake + 3 pts mistake + 2 pts several mistakes + 1 pts something is right QUESTION 5 5 308 5 5 / 5 ✓ + 5 pts Correct + 4 pts small mistake + 3 pts mistake + 2 pts several mistakes + 1 pts something is right QUESTION 6 6 308 20 5 / 5 ✓ + 5 pts Correct + 4 pts small mistake + 3 pts mistake + 2 pts several mistakes + 1 pts something is right QUESTION 7 7 318 4 5 / 5 ✓ + 5 pts Correct + 4 pts small mistake + 3 pts mistake + 2 pts several mistakes + 1 pts something is right + 0 pts missing problem

QUESTION 8 8 318 9 5 / 5 ✓ + 5 pts Total score - 1 pts small mistake - 1.5 pts did not successfully check it is a vector space (in particular, need to check closed under addition and scalar multiplication ) - 1.5 pts incorrect basis. Note that the basis should consist of three 2X2 matrixs QUESTION 9 9 318 22 5 / 5 ✓ + 5 pts Correct + 3.5 pts did not correctly explain why it is a vector space( at least need to check the addition of two valid vectors is still valid, where valid means orthogonal to (2,0,1)) Important remark: many students did check the "Commutativity" and "Associativity" of addition, this is good, but it is different from "closed under addition" ! + 3.5 pts did not correctly find the vector space (a basis is { (-1/2,0,1), (0,1,0) }) + 2 pts both Rubric 2 and Rubric 3 apply + 0 pts missing problem Page 2

1 287 5 5 / 5 ✓ + 5 pts Correct + 4 pts small mistake + 3 pts mistake + 2 pts several mistakes + 1 pts something is right Page 4

3 300 12 5 / 5 ✓ + 5 pts Correct + 4 pts small mistake + 3 pts mistake + 2 pts several mistakes + 1 pts something is right Page 8

4 300 22 5 / 5 ✓ + 5 pts Correct + 4 pts small mistake + 3 pts mistake + 2 pts several mistakes + 1 pts something is right Page 10