APPM 2360 Midterm: appm2360fall2017exam2_sol
Document Summary
On the front of your bluebook write: (1) your name, (2) your instructor"s name, (3) your lecture section number and (4) a grading table. Text books, class notes, cell phones and calculators are not permitted. A one page letter sized crib sheet is allowed. Problem 1: (30 points) true/false (answer true if it is always true, otherwise answer false. 0 0 x1 x2 x3 (d) (6 points) if 4 vectors in r4 are linearly independent, they span r4. (e) (6 points) let a, p , and m all be invertible matrices. 1(cid:21) is a vector (ap p m ) 1 = a 1p 1p 1m 1. Solution: (a) false. det(ki) = k4. (b) true. Since both are invertible, |a| 6= 0, |b| 6= 0, and so |ab| = |a||b| 6= 0. (c) false. W does not contain the zero vector ~0 = . Since the vectors are linearly independent, the matrix a that has these vectors as columns is invertible.
