o Sprint LTE 8:10 AM 93% tlmadsen people ysu.edu C MATH 3720-01: Linear Algebra

Question

o Sprint LTE 8:10 AM 93% tlmadsen people ysu.edu C MATH 3720-01: Linear Algebra Fall 2014, Y State University Homework 11 due November 17 Problem A. Let To R2 R2 be the linear transformation with cos(6) sin(0) sin(0) cos (6) Find all eigenvalues and corresponding e of To. Do we have eigen- values for all values of 8? How does this make sense geometrically? Problems from the book 3.6: 36, 37 4.2: 16, 26, 27, 32, 33, 34, 58, 65 Page 283-281: do problems 2 and 3(a), 3(b), 3(c), 3(d), 3() 4.3: 1, 3, 5, 7, 17, 18, 19

Explanation / Answer

A= COS(T) -SIN(T) SIN(T) COS(T) A-LI= COS(T)-L -SIN(T) SIN(T) COS(T)-L |A-LI|=L^2+COS^2(T)-2LCOS(T)+SIN^2(T)=0 L^2-2LCOS(T)+1=0 L1 = 0.5[2COS(T)+{4COS^2(T)-4]^0.5] = COS(T)+ISIN(T)=E^(IT) L2= 0.5[2COS(T)-{4COS^2(T)-4]^0.5] = COS(T)-ISIN(T)=E^(-IT) ARE THE 2 EIGEN VALUES THE EIGEN VALUES EXIST IN COMPLEX PLANE IF YOU ARE TALKING OF ONLY REAL VALUES , THEN FOR T=0,PI,2PI,

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