MATH 304 Midterm: MATH 304 Binghamton Math304 Fall2018 Exam2V1 Solutions

• School: Binghamton University
• Department: Mathematical Science
• Course: MATH 304
• Professor: All

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Then the reduced row echelon form of a is . 0 (a) (4 pts) find a basis for col(a). Solution: since a row reduced to the matrix above with pivot columns 1 and 2, a basis for col(a) can be {col1(a), col2(a)}. (b) (4 pts) find a basis for nul(a). Solution: since a row reduced to the matrix above, the solutions to ax = 0 are r + 2s. Nul(a) = r s a basis for nul(a). R5 (cid:12)(cid:12)(cid:12)(cid:12) r, s r so. 1 is (c) (2 pts) find the dimension of row(a). Solution: since there are 2 non-zero rows in the rref (a), dim(row(a)) = 2. , vk} be a set of k vectors in rn. Consider the following statements. (a) the set {v1, v2, . , vk} is linearly independent. (b) {v1, v2, . , vk} is linearly dependent. (c) {v1, v2, . , vk} spans rn. (d) {v1, v2, .