(Penalty 10 points for missing staple.) [First Name] Math 2333: [Last Name] THQ 03, 10-09-16, 14:48 [Net ID] Math 2333: THQ 03 Instructions: 1. Fill in the requested information on the line above. 2. This handout is due at the beginning of class on Wednesday. 3. This handout must be printed out and stapled. You may print it double sided. 4. There will be a one point penalty for each minute for late submissions. 5. Your work must be hand written on this handout. 6. Refer to the textbook for definitions and problem statements. 7. You must show all work and check your answers. You may receive zero or reduced points for insufficient work. 8. Your work must be neatly organized and written. You may receive zero or reduced points for sloppy work. 9. Sometimes only a subset of these questions may be graded. You will not be told which questions will be graded in advance. 10. Students are not allowed to ask the Math Lab for assistance for any homework assignments. [Section] Page 2 of 6 Math 2333: Question 1 2 3 4 5 Total Points 12 12 12 12 12 60 THQ 03, 10-09-16, 14:48 Score 1. (12 points) Consider the following vectors from R3 : (2, 6, 5) (3, 3, 7) (6, 5, 4) (4, 6, 9) Determine whether these form a basis for R3 . Give a short reason, but do not work too hard. Note: You do not have to use Gauss-Jordon. Page 3 of 6 Math 2333: THQ 03, 10-09-16, 14:48 2. (12 points) Consider all vectors from R5 of the following form: (a + 3b, 2a 5b, a, 4a + 6b, b) (a) Given that these form a subspace (so you don't have to show that), find a basis for this subspace. (b) What is the dimension of that subspace? Page 4 of 6 Math 2333: THQ 03, 10-09-16, 14:48 3. (12 points) Consider the following vectors from R4 : (3, 6, 1, 5) (2, 2, 6, 8) (1, 8, 8, 4) Determine whether these form a basis for R3 . Give a short reason, but do not work too hard. Note: You do not have to use Gauss-Jordon. Page 5 of 6 Math 2333: THQ 03, 10-09-16, 14:48 4. (12 points) Suppose that vectors from R4 , u, v, w and x, are given, and placed into a matrix as it's four columns. After applying Gauss-Jordon to that 4 4 matrix we reach the following matrix: 1 0 [ u | v | w | x ] = = 0 0 0 5 1 2 0 0 0 0 0 0 . 1 0 From this result, do the vectors u, v, w and x constitute a basis for R4 ? Explain your answer. Page 6 of 6 Math 2333: THQ 03, 10-09-16, 14:48 5. (12 points) Now suppose that different vectors from R4 , u0 , v0 , w0 and x0 , are given, and placed into a matrix as it's four columns. After applying Gauss-Jordon to that 4 4 matrix we reach the following matrix: 1 0 [ u0 | v0 | w0 | x0 ] = = 0 0 0 0 0 1 0 0 . 0 1 0 0 0 1 From this result, do the new set of vectors, u0 , v0 , w0 and x0 , constitute a basis for R4 ? Explain your