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Determine the eigenvalues and as many linearly independent eigenvectors as you can of the matrix A 3 1 -5 0 3 0 0 -30 0 -1 5 6 0 over R. State whether or not it is diagonalizable over R and give reasons for your answer.

Determine the eigenvalues and as many linearly independent eigenvectors as you can of the matrix A 3 1 -5 0 3 0 0 -30 0 -1 5 6 0 over R. State whether or not it is diagonalizable over R and give reasons for your answer.

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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Suppose that 0 : V → W and &: W → V are linear mappings with the property chat &(0(v)) = v for all v € V. Show that Imker {0}. That is, the ntersection of the image of 0 and the kernel of is the zero vector. =
Transcribed Image Text:Suppose that 0 : V → W and &: W → V are linear mappings with the property chat &(0(v)) = v for all v € V. Show that Imker {0}. That is, the ntersection of the image of 0 and the kernel of is the zero vector. =
Determine the eigenvalues and as many linearly independent eigenvectors as you can of the matrix A ( 3 1 -5 0 6 0 0 0 -3 0 -1 5 3 over R. State whether or not it is diagonalizable over R and give reasons for your answer.
Transcribed Image Text:Determine the eigenvalues and as many linearly independent eigenvectors as you can of the matrix A ( 3 1 -5 0 6 0 0 0 -3 0 -1 5 3 over R. State whether or not it is diagonalizable over R and give reasons for your answer.
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