MATH 141 Midterm: MATH141 South Carolina 141 f 05 3
Document Summary
Full credit may not be given for an answer alone. You may use the backs of the pages or the extra pages for scratch work. Students who, for whatever reason, submit work not their own will ordi- narily be required to withdraw from the college. 1: (10 points) find the reduced row echelon form of the matrix. In this and in any problem where you do gaussian elimination, label your row operations to receive full or partial credit. 2: (10 points) find the parametric form of the solution to the system of linear equations x1 + 2x2 + 3x3 + x4 = 8 x1 + 3x2. 4: (15 points) a is the same matrix as before: Find a diagonal matrix d and an invertible matrix p such that a = p dp 1. 5: (10 points) let (i) find and classify all critical points of the function. f (x, y) = xy.
