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H2. Let A5 be the matrix 22-2 5 1-3 15-3 A5 = (a) Use the eigenvalues of A5 to show that A5 is nilpotent. (b) Determine the smallest positive exponent k such that A5K = 0.

H2. Let A5 be the matrix 22-2 5 1-3 15-3 A5 = (a) Use the eigenvalues of A5 to show that A5 is nilpotent. (b) Determine the smallest positive exponent k such that A5K = 0.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.1: Eigenvalues And Eigenvectors
Problem 53E
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H2 part b
Log In Sep 07 Sep Read your lecture notes and do H2. Let A5 be the matrix [22 -2 A5 = 51 -3 15-3 (a) Use the eigenvalues of A5 to show that A5 is nilpotent. (b) Determine the smallest positive exponent k such that A5k = 0. H3. (a) Determine which of the matrices A1, ..., A4 from Questions 2.2.1 and H1 are nilpotent. (b) For each matrix in (a) that is nilpotent, determine the smallest positive exponent k such that Ajk = 0. Sec 2.3: 2, 3 (assume the notation in question 3 is referring to question 2). If any of the mathematics does not display properly (e.g., an error message received), compare with this file. Recall that a scan of the instructor's lecture notes can be found in the Modules section of our Canvas portal. Quiz 1 opens today; it is due Sept 18. Read your lecture notes and do q
Transcribed Image Text:Log In Sep 07 Sep Read your lecture notes and do H2. Let A5 be the matrix [22 -2 A5 = 51 -3 15-3 (a) Use the eigenvalues of A5 to show that A5 is nilpotent. (b) Determine the smallest positive exponent k such that A5k = 0. H3. (a) Determine which of the matrices A1, ..., A4 from Questions 2.2.1 and H1 are nilpotent. (b) For each matrix in (a) that is nilpotent, determine the smallest positive exponent k such that Ajk = 0. Sec 2.3: 2, 3 (assume the notation in question 3 is referring to question 2). If any of the mathematics does not display properly (e.g., an error message received), compare with this file. Recall that a scan of the instructor's lecture notes can be found in the Modules section of our Canvas portal. Quiz 1 opens today; it is due Sept 18. Read your lecture notes and do q
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