MATH 461 Midterm: MATH461 BOYLE-M SPRING2006 0101 MID SOL

• School: University of Maryland
• Department: Mathematics
• Course: MATH 461
• Professor: All

Document Summary

Math 461-01** spring 2006 exam 1. Answer each question on a separate sheet of paper. On each sheet, put your name, your section leader"s name and your section meeting time. Put a box around your nal answer to each part. You must be careful on arithmetic check. You may assume given matrix equations are well de ned (i. e. the matrix sizes are compatible): (15 pts) find all solutions for the following system of equations: x1 + 2x2 + 2x3 x4 = 2. Form the corresponding augmented matrix and perform elementary row operations successively to reach the reduced row-echelon form: The solution set of the system corresponding to the augmented matrix does not change as we reduce as above. So the general solution, parametrized by the free variable x2, is. A 3 4 matrix has 3 columns: true. If u is an invertible matrix, then the equations u ax = 0 and ax = 0 have the same solution set: false.