MATH 0280 Midterm Examination I, Sample 1 - ANSWERSProblem 1. NoProblem 2. Linearly dependent: 2¯v1+ ¯v2− ¯v3=¯0Problem 3. Matrices A, C and S are not elementary, matrices B, Dand T are elementary.B−1=1 0 50 1 00 0 1, D−1=1 0 00 0 10 1 0, T−1=1/17 0 00 1 00 0 1.Problem 4. A−1=−4 −1/2 5/2−1 1/2 1/22 0 −1Problem 5. A = a100 a4!, where a1and a4are any numbers.Problem 6.a) 2x + y − z + 1 = 0.b) NOTE: there are multiple forms of the correct answer. One of thepossible forms:xyz=−230+ t0111Problem 7.1 00 10 00 0,1 ∗0 00 00 0,0 10 00 00 0,0 00 00 00 0, where * is any number.Problem 8.xyz=19/2−5/20+ t−5/23/21Problem 9.a) E =1 0 01 1 00 0 1;b) X = E2E1=1 0 00 1 00 −3 1·1 0 01 1 00 0 1=1 0 01 1 0−3 −3 1Problem 10. A and B are row-equivalent, since their Reduced RowEchelon forms are both equal to I = 1 00 1!.The following sequence of the opeations converts A to B(NOTE: This sequence is not unique. To check your answer, apply youroperations in the listed order starting from the matrix A. You are supposed2to get B after you apply all your operations):1. R2→ R2− R12. R1←→ R23. R2→ R2− 2R14. R1→ (−1)R15. R2→ 3R26. R2→ R2−