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[10 010 0 2 1 000 2 Answer the questions below for the matrix A = 0 (a) Find all eigenvalues of A. (b) For each eigenvalue A₁, we define the eigenspace Ex₂ = null (A - X; I) to be the nullspace of A-XI. For each eigenvalue A₁, use the rank-nullity theorem to calculate dim(Ex) and find a basis for Ex. Recall that the rank-nullity theorem says that, for an m by n matrix T, rank(T) + nullity(T) = n. (c) Is A diagonalizable? Explain.

[10 010 0 2 1 000 2 Answer the questions below for the matrix A = 0 (a) Find all eigenvalues of A. (b) For each eigenvalue A₁, we define the eigenspace Ex₂ = null (A - X; I) to be the nullspace of A-XI. For each eigenvalue A₁, use the rank-nullity theorem to calculate dim(Ex) and find a basis for Ex. Recall that the rank-nullity theorem says that, for an m by n matrix T, rank(T) + nullity(T) = n. (c) Is A diagonalizable? Explain.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Answer the questions below for the matrix A = = 0 0 0 0 1 0 0 (a) Find all eigenvalues of A. (b) For each eigenvalue A₁, we define the eigenspace 0 0 0 0 2 1 0 2 Ex = null (A - A¡I) to be the nullspace of A-XI. For each eigenvalue A₁, use the rank-nullity theorem to calculate dim(Ex) and find a basis for Ex. Recall that the rank-nullity theorem says that, for an m by n matrix T, rank(T) + nullity (T) = n. (c) Is A diagonalizable? Explain.
Transcribed Image Text:Answer the questions below for the matrix A = = 0 0 0 0 1 0 0 (a) Find all eigenvalues of A. (b) For each eigenvalue A₁, we define the eigenspace 0 0 0 0 2 1 0 2 Ex = null (A - A¡I) to be the nullspace of A-XI. For each eigenvalue A₁, use the rank-nullity theorem to calculate dim(Ex) and find a basis for Ex. Recall that the rank-nullity theorem says that, for an m by n matrix T, rank(T) + nullity (T) = n. (c) Is A diagonalizable? Explain.
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