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Let A = 1 2 (a) Find the characteristic polynomial of A. (b) Find the eigenvalues of A. (c) Find a basis for each eigenspace of A. resou (d) For each eigenyalue, state its algebraic and geometric multiplicity, Ex Qursel

Let A = 1 2 (a) Find the characteristic polynomial of A. (b) Find the eigenvalues of A. (c) Find a basis for each eigenspace of A. resou (d) For each eigenyalue, state its algebraic and geometric multiplicity, Ex Qursel

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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Need help with parts (d), (e) and (f). Thank you :)

 

- } 7. Let A = (a) Find the characteristic polynomial of A. (b) Find the eigenvalues of A. (c) Find a basis for each eigenspace of A. resour (d) For each eigenvalue, state its algebraic and geometric multiplicity. Explain your answer. (e) Is A orthogonally diagonalizable? If so, find a matrix P which orthogonally diagonalizes A. (f) Is the conic section defined by the equation x" Ax = 1 an ellipse or an hyperbola? Why? (g) How many paths of length n exist between vertices 1 and 2 in the graph with adjacency matrix A? ourseHo
Transcribed Image Text:- } 7. Let A = (a) Find the characteristic polynomial of A. (b) Find the eigenvalues of A. (c) Find a basis for each eigenspace of A. resour (d) For each eigenvalue, state its algebraic and geometric multiplicity. Explain your answer. (e) Is A orthogonally diagonalizable? If so, find a matrix P which orthogonally diagonalizes A. (f) Is the conic section defined by the equation x" Ax = 1 an ellipse or an hyperbola? Why? (g) How many paths of length n exist between vertices 1 and 2 in the graph with adjacency matrix A? ourseHo
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