APPM 2360 Midterm: appm2360spring2013exam2_sol
Document Summary
On the front of your bluebook, write (1) your name, (2) your instructor"s name, (3) your lecture number, and (4) a grading table. You"re allowed one sheet (letter-sized, front and back) of notes. You are not allowed to use textbooks, class notes, or calculators. Problem #1 (20 points): consider the following system: x1 + x3 = 1, What is the general solution? (5 points) (d) what is a basis for the solution space of a x = 0? (3 points) Solution: (a) e matrix equation for this system is. 1 2 3 3 (b) using elementary row operations we get (c) rewriting the rref augmented matrix, we have. 0 x1 + x3 = 1 and x2 2x3 = 2. Next, note that x1 and x2 are basic variables. Solving for these, we have x1 = p + 1, x2 = 2p 2, and x3 = p.
