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CategoryMath
SubjectAlgebra
DifficultyUndergraduate
StatusSolved
More InfoCalculus Homework Help
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Hi, there is some problem with the matrix. Need to find eigenvalues, eigenvectors, chains of eigenvectors and create diagonalization matrix G and compute G^-1 *D*G. See details in the attachment. Solve them step by step, please!

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Algebra Assignment Description Image [Solution]
For the following matrices, find: ● All eigenvalues and state their multiplicity. • As many independent eigenvectors as possible. • A complete set of generalized eigenvectors. • Describe all of the chains of eigenvectors. A -2 0 0 0 -2 0 0 -2 0 0 -2 and 0 -2 1 0 0 -2 0 0 0 - 0 -2 1 0 -2 A= B = D = Finally, use the (generalized) eigenvalues that you found for D to create the ‘diagonal- ization' matrix G and compute G-¹DG. A note on inverses: Given an invertible matrix A21 = a12a33 - a13a32, A31 = a12a23 - a13a22, A-¹ a11 a12 a13 a23 a21 a22 a31 a32 a33, we can use the adjugate matrix Adj(A) to define the inverse of A, where A11 - A21 A31 Adj (A) = -A12 A22 - A32 A13 - A23 A33 and A¡¡ is the determinant of the 2 × 2 matrix we get from deleting the ith row and jth column in A. For example, 0 1 det (A) 0 0 1 -2 0 0 -2 0 0 -2 -2 −1 0 -2 0 0 -2 - Adj(A). 2 A22 = a11a33 - a13a31. Note that this is slightly different from what I wrote in lecture. This is correct, while the lecture was wrong. (Precisely: this is the transpose of what I wrote in lecture.) With this definition,

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