Problem 1PP: Let A=[115207353] and u=[732] Is u in Nul A? Is u in Col A? Justify each answer. Problem 2PP: Given A=[010001000], find a vector in Nul A and a vector in Col A. Problem 3PP: Suppose an n n matrix A is invertible. What can you say about Col A? About Nul A? Problem 1E: Exercises 14 display sets in 2. Assume the sets include the bounding lines. In each case, give a... Problem 2E: Exercises 14 display sets in 2. Assume the sets include the bounding lines. In each case, give a... Problem 3E: Exercises 14 display sets in 2. Assume the sets include the bounding lines. In each case, give a... Problem 4E: Exercises 1-4 display sets in 2. Assume the sets include the bounding lines. In each case, give a... Problem 5E: Let v1 = [235], v2 = [458], and w = [829]. Determine if w is in the subspace of 3 generated by v1... Problem 6E: Let v1 = [1243], v2 = [4797], v3 = [5865], and u = [41075]. Determine if u in the subspace of 4... Problem 7E: Let v1 = [286], v2 = [387], v3 = [467], p = [41011], and A = [v1, v2, v3]. a. How many vectors are... Problem 8E: Let v1 = [306], v2 = [223], v3 = [063], and p = [1149]. Determine if p is in Col A, where A = [v1,... Problem 9E: With A and p as in Exercise 7, determine if p is in Nul A. 7. Let v1 = [286], v2 = [387], v3 =... Problem 10E: With u = (2, 3, 1) and A as in Exercise 8, determine if u is in Nul A. 8. Let v1 = [306], v2 =... Problem 11E: In Exercises 11 and 12. give integers p and q such that N'ul A is a subspace of p and Col A is a... Problem 12E: In Exercises 11 and 12. give integers p and q such that N'ul A is a subspace of p and Col A is a... Problem 13E: For A as in Exercise 11, find a nonzero vector in Nul A and a nonzero vector in Col A. In Exercises... Problem 14E: For A as in Exercise 12, find a nonzero vector in Nul A and a nonzero vector in Col A. 12. A =... Problem 15E: Determine which sets in Exercises 15-20 are bases for 2? or 2. Justify each answer. 15. [52], [103] Problem 16E: Determine which sets in Exercises 15-20 are bases for 2 or 3. 16. [46], [23] Problem 17E: Determine which sets in Exercises 15-20 are bases for 2? or 3. Justify each answer. 17. [012],... Problem 18E: Determine which sets in Exercises 15-20 are bases for 2? or 3. Justify each answer. 18. [112],... Problem 19E: Determine which sets in Exercises 15-20 are bases for 2? or 3. Justify each answer. 19. [381], [625] Problem 20E: Determine which sets in Exercises 15-20 are bases for 2? or 3. Justify each answer. 20. [167],... Problem 21E: In Exercises 21 and 22, mark each statement True or False. Justify each answer. 21. a. A subspace of... Problem 22E: a. A subset H of n is a subspace if the zero vector is in H. b. Given vectors v1,, vp in n. the set... Problem 23E: Exercises 23-26 display a matrix A and an echelon form of A. Find a basis for Col A and a basis for... Problem 24E: Exercises 23-26 display a matrix A and an echelon form of A. Find a basis for Col A and a basis for... Problem 25E: Exercises 23-26 display a matrix A and an echelon form of A. Find a basis for Col A and a basis for... Problem 26E: Exercises 23-26 display a matrix A and an echelon form of A. Find a basis for Col A and a basis for... Problem 27E: Construct a nonzero 3 3 matrix A and a nonzero vector b such that b is in Col A, but b is not the... Problem 28E: Construct a nonzero 3 3 matrix A and a vector b such that b is not in Col A. Problem 29E: Construct a nonzero 3 3 matrix A and a nonzero vector b such that b is in Nul A. Problem 30E: Suppose the columns of a matrix A = [a1 ap] are lineally independent. Explain why {a1, ,ap} is a... Problem 31E: In Exercises 31-36, respond as comprehensively as possible, and justify your answer. 31. Suppose F... Problem 32E: In Exercises 31-36. respond as comprehensively as possible, and justify your answer. 32. If R is a 6... Problem 33E: In Exercises 31-36, respond as comprehensively as possible, and justify your answer. 33. If Q isa4 ... Problem 34E: In Exercises 31-36, respond as comprehensively as possible, and justify your answer. 34. If P is a 5... Problem 35E: In Exercises 31-36, respond as comprehensively as possible, and justify your answer. 35. What can... Problem 36E: In Exercises 31-36, respond as comprehensively as possible, and justify your answer. 36. What can... Problem 37E: [M] In Exercises 37 and 38, construct bases for the column space and the null space of the given... Problem 38E: [M] In Exercises 37 and 38, construct bases for the column space and the null space of the given... format_list_bulleted