Find the standard Matrix Find the standard matrix for the following Q(x) quadratic form Find the eigenvalues Calculate the eigenvalues for the above standard matrix Determine the larger eigenvalue: 19 Determine the second eigenvalue: e Determine the eigenvectors Next, we determine the corresponding eigenvectors for each eigenvalue. At this point we do not yet need to normalize our eigenvectors, but we will do that in a later step Pmatrix If the following vectors are the respective eigenvectors of A, determine the orthogonal matrix P such that A PDP™ With [2] as the first vector in P Hint: Quadratic form new equation Q(x) = 10z² + 122,2₂ +152 10 6 6 The first eigenvector for A=19 has the form (1) Assuming that z=2, enter the eigenvector for A = 19 = 2 3 4 The next eigenvector for A-6 has the form ty=1). Assuming that z=-3, enter the eigenvector for X = 6 A 3 2 2isgrt13 15 3/sqrt13 --3 -2

Find the standard Matrix Find the standard matrix for the following Q(x) quadratic form Find the eigenvalues Calculate the eigenvalues for the above standard matrix Determine the larger eigenvalue: 19 Determine the second eigenvalue: e Determine the eigenvectors Next, we determine the corresponding eigenvectors for each eigenvalue. At this point we do not yet need to normalize our eigenvectors, but we will do that in a later step Pmatrix If the following vectors are the respective eigenvectors of A, determine the orthogonal matrix P such that A PDP™ With [2] as the first vector in P Hint: Quadratic form new equation Q(x) = 10z² + 122,2₂ +152 10 6 6 The first eigenvector for A=19 has the form (1) Assuming that z=2, enter the eigenvector for A = 19 = 2 3 4 The next eigenvector for A-6 has the form ty=1). Assuming that z=-3, enter the eigenvector for X = 6 A 3 2 2isgrt13 15 3/sqrt13 --3 -2

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 78E: Find all values of the angle for which the matrix A=[cossinsincos] has real eigenvalues. Interpret...

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