MATH 291 Midterm: MATH 290 Drexel q1 sol
Document Summary
No calculators allowed during exams and quizzes: solve the following linear system using matrix methods: x1 + 2x2 + x3 = 2 x1 x2 2x3 = 2. 0 0 1 6 x1 + 2x2 + x3 = 2 x2 + x3 = 0 x3 = 6 x1 = 2 2x2 x3 x2 = x3 x3 = 6 (unique) solution: x1 = 1: the augmented matrix of a linear system has been reduced by row operations to the form shown. By continuing the reduction using appropriate row operations, determine whether the system is consistent or not. The system is consistent, so at least one solution exists. There are no free variables (there are no variables corresponding to non-pivot columns), so the solution is unique: let a1 = The last row implies that the system is inconsistent. Thus, b is not a linear combination of a1, a2, a3. That is, b is not in span{a1, a2, a3}.
