ENGM 2022 Study Guide - Midterm Guide: Wronskian, Partial Fraction Decomposition, Step Function

• School: Dalhousie University
• Department: Engineering Mathematics
• Course: ENGM 2022
• Professor: All

Document Summary

4 2 1 (1) [8] let a = (a) [2] find the eigenvalues of a. (b) [6] find an eigenvector for each eigenvalue. The characteristic polynomial of a is p(z) = z2 tr(a)z + det(a) = z2 6z + 13 = (z 3)2 + 22 . (cid:19) A (3 + i2)i = (cid:18)2 i2. The eigenvalues of a are the roots of this polynomial, which are 3 + i2 and 3 i2. (cid:19) in computing the eigenvalue or in computing the matrix(cid:0)a (3 + i2)i(cid:1)!) Because these matrices are conjugates, it su ces to check that the determinant of the rst of these matrices is zero. (if it is not then you have made a mistake either. A is a 2 2 matrix, we can read o from their rst columns that eigenpairs of a are (cid:18)2 + i2. 3 + i2 , (cid:19)(cid:19) (cid:19)(cid:19) (cid:18)1 + i 1 (cid:18) 2 1 + i (cid:18) (cid:18)