CO350 Assignment 1 Due: May 14 at 2pm. Submit your assignment in drop box 2 (opposite MC4066) by 2pm. Your full name, stu-dent ID number, the course number, and the name of your instructor should all be clearly visible on the front of your assignment. You may discuss the assignment questions with other students, but you must write your solutions up independently, and all submitted work must be your own. Exercise 1: (linear algebra review.) Let A ∈ R m × n and b ∈ R m . (a) Show that, if the system Ax = b has a solution and the columns of A are not linearly independent, then Ax = b has inﬁnitely many solutions. (b) Show that, if the system Ax = b has a solution and the columns of A are linearly independent, then Ax = b has a unique solution. Exercise 2: (linear programming) Let A ∈ R m × n , b ∈ R m , and let c ∈ R n . Show that, if max( c t x : Ax = b, x ≥ 0) has two solutions, then it has inﬁnitely many solutions. Exercise 3:
This is the end of the preview.
access the rest of the document.
linear program, student ID number, infinitely many solutions, Linear Algebra Review