MATH 340 Midterm: MATH 340 UW Madison 340Spring 11Solutions1

• School: UW-Madison
• Department: Mathematics
• Course: MATH 340
• Professor: All

Document Summary

Suppose, for some system of equations, the augmented matrix is row equivalent to (10 points) Give all solutions to the system of equations. The coe cient matrix is in ref but not rref. We could either read the solutions from the matrix as it is, or convert it to rref. I will do it from the matrix as it is: the last row says x6 = 5 so there is no choice about that. The next-to-last row says x5 + 3x6 = 4, and we have x6 = 5, so we must have x5 = 4 3 5 = 11. The third row says x4 + 2x6 = 3, so again using our value for x6 we have x4 = 3 2 5 = 13. The third column has no leading entry, so the value for x3 is arbitrary: let it be some number .