APPM 2360 Midterm: appm2360summer2014exam2
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On the front of your bluebook write: (1) your name, (2) your student id number, (3) recitation section, (4) your instructor"s name, and (5) a grading table. Books, class notes, cell phones, and calculators are not permitted. Problem 1: (20 points) let k be a real number and consider the system of equations: Problem 2: (20 points) matrix operations: (a) suppose a, b, c are n n matrices such that det(a) = 3, det(b) = 1, and det(c) = 0. Either calculate det(ab2c 1) or explain why it doesn"t exist. (b) let a = . Calculate abt . (c) let a be an n n invertible matrix satisfying a3 + 2a = i. Problem 3: (20 points) eigenvalues and eigenvectors (a) compute the eigenvalues and eigenvectors for the matrix: (cid:18)0 1. 3 2(cid:19) (b) give the eigenvalues of the matrix. Problem 4: (20 points) vector spaces, basis, and dimension. (a) consider each of the following sets.
