MATH 461 Midterm: MATH461 BOYLE-M SPRING2006 0101 MID EXAM
15 Feb 2019
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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. 2! are linearly dependent. (b) (4 pts) suppose t : r3 r3. Let ei denote the 3 1 column vector whose ith entry is 1 and whose other entries are zero. Ax = 0 corresponds to a system of equations in the variables x1, x2, . which are the entries of x. Is the system necessarily consistent? (b) (8 pts) suppose a matrix a is row equivalent to the following matrix b:
