3 Eigenvalues and Eigenvectors Represent the matrix A as A = V-¹AV, where A = diag(A₁..... An) is the diagonal matrix with the eigenvalues A E C of A on its diagonal, and V = [...] is the matrix whose columns are the eigenvectors, such that 1 E C is an eigenvector associated with the eigen- value A. Whenever possible, normalize the eigenvector so that the first coordinate of the vector is 1 (if the first coordinate is 0, normalize it so that the second coordinate is 1). -5 3 (a) A= 18 (b) A= 1 Calculate A² and A²-3A +27. Calculate trace(A) and det(A). -6 [2 -0.5] (c) A= (Can you conclude what is A¹ without any additional calculation?) 3 -0.5
3 Eigenvalues and Eigenvectors Represent the matrix A as A = V-¹AV, where A = diag(A₁..... An) is the diagonal matrix with the eigenvalues A E C of A on its diagonal, and V = [...] is the matrix whose columns are the eigenvectors, such that 1 E C is an eigenvector associated with the eigen- value A. Whenever possible, normalize the eigenvector so that the first coordinate of the vector is 1 (if the first coordinate is 0, normalize it so that the second coordinate is 1). -5 3 (a) A= 18 (b) A= 1 Calculate A² and A²-3A +27. Calculate trace(A) and det(A). -6 [2 -0.5] (c) A= (Can you conclude what is A¹ without any additional calculation?) 3 -0.5
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.2: Diagonalization
Problem 45E
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