MATH 3000 Midterm: MATH 331 Mizzou Exam 2 Solutions

• School: Mizzou
• Department: Mathematics
• Course: MATH 3000
• Professor: All

Document Summary

Math 331 quiz 4 solutions: the set {v1, . , vn} is a basis for v if (i) v = span(v1, . , vn} is linearly independent: suppose that v = span(v1, v2, v3, v4) and the set {v1, v2, v3, v4} is linearly dependent. What are the possible dimensions of v . According to theorem d(iii) (or theorem 3. 4. 4), any spanning set for v can be pared down to give a basis. Since the given set is linearly dependent, it cannot be a basis itself. What is dim(s)? (you do not need to verify that s is a subspace. ) This is similar to a homework problem, but please note that it is a subspace of p4, rather than p3. S = {a + bx + cx2 + dx3 | a + b + c + d = 0 and a b + c d = 0}. The equations come from plugging in x = 1 and x = 1.