MATH 2568 Final: Math 2568 m2568au17final_sample

• School: Ohio State University
• Department: Mathematics
• Course: MATH 2568
• Professor: All

Document Summary

Problems: give the detailed de nition of vector spaces, consider the following 3 3 matrix. Find an invertible 3 3 matrix s and a diagonal 3 3 matrix d such that. As = sd: let a be a 3 3 matrix with 3 distinct eigenvalues. Denote by c0 + c1x + c2x2 + c3x3 the characteristic polynomial of a. Show that c0i3 + c1a + c2a2 + c3a3 = o: determine whether the following matrix is invertible or not: If a is invertible, compute a 1: show that the set of polynomials in x of degree at most 5 is a vector space, give the de nition of orthogonal matrices.