CS 1110 Midterm: CS 1110 Cornell 2013 Fall prelim1 Exams2012 Fall prelim1 answers

• School: Cornell University
• Department: Computer Science
• Course: CS 1110
• Professor: All

Document Summary

In each part, you are given the augmented matrix of a linear system. The coe cient matrix is already in reduced row eche- lon form. Determine if the system is consistent, and if it is consistent nd all solutions. (a. ) (b. ) (c. ) Answer : (x, y, z) = (5, 1, 3) Answer : the system is inconsistent, because of the last row. The variables x1,x3 and x5 are leading variables and x2 and x4 are non-leading or free variables. Say x2 = and x4 = . The third row of the matrix gives us the equation x5 = 3. The second row of the matrix gives the equation x3 2x4 = 0, so x3 = 2x4 = 2 . The rst row of the matrix gives the equation x1 x2 + 2x4 = 1, and so x1 = 1 + x2 2x4 = 1 + 2 .