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(b) Find the so vy0)= 5. 101. Solve the system y= 3y + + y = +3y+ y 2+3 102. (a) Solve the system +3

(b) Find the so vy0)= 5. 101. Solve the system y= 3y + + y = +3y+ y 2+3 102. (a) Solve the system +3

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 70EQ
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101
(b) Find the solution that satisfies the initial conditions 330 Chapter 5 Eigenvalues and Elgenvectors (b) Show that if A is a diagonalizable matrix with nonneg- Differential Equations ative eigenvalues, then there is a matrix S such that S= A. 99. (a) Solve the system (c) Find a matrix S such that S=A, given that 2y-3y -4y + » 1. 3. A =|0 4 5 9. V (0) 0, v(0) 0. 95. Prove that if u and v are vectors in C, then 100. (a) Solve the system u+ u =-2v-4 vy (b) Find the solNion that satisfies the conditions y, (0) 10. 0) = 5. 96. (a) Show that if 0 0T then sin 101. Solve the system =3v + + y V= y +3y; + sin cos# has no real egemalues and consequently no real eigen- vectors. = + + 3y (b) Give a gcometne explanation of the result in part (al. 102. (a) Solve the system 97. The two parts of this exercise lead you through a proof of Theorem 5 38 = +3v = 2v + 4 (hi Find the solution satisfying the initial conditions vi0 S and y (0) = 6 (ar For notational simplicity, let 103. Show that if A is diagonalizable and and let u Reixind Im, se P u Show 16:20 that the relationsbip AN Implies that ENG 2021/09/23 IN
Transcribed Image Text:(b) Find the solution that satisfies the initial conditions 330 Chapter 5 Eigenvalues and Elgenvectors (b) Show that if A is a diagonalizable matrix with nonneg- Differential Equations ative eigenvalues, then there is a matrix S such that S= A. 99. (a) Solve the system (c) Find a matrix S such that S=A, given that 2y-3y -4y + » 1. 3. A =|0 4 5 9. V (0) 0, v(0) 0. 95. Prove that if u and v are vectors in C, then 100. (a) Solve the system u+ u =-2v-4 vy (b) Find the solNion that satisfies the conditions y, (0) 10. 0) = 5. 96. (a) Show that if 0 0T then sin 101. Solve the system =3v + + y V= y +3y; + sin cos# has no real egemalues and consequently no real eigen- vectors. = + + 3y (b) Give a gcometne explanation of the result in part (al. 102. (a) Solve the system 97. The two parts of this exercise lead you through a proof of Theorem 5 38 = +3v = 2v + 4 (hi Find the solution satisfying the initial conditions vi0 S and y (0) = 6 (ar For notational simplicity, let 103. Show that if A is diagonalizable and and let u Reixind Im, se P u Show 16:20 that the relationsbip AN Implies that ENG 2021/09/23 IN
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