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A matrix has characteristic polynomial p(X) = (A + 4) (A + 9)³. Fill in the blanks with the best answer for each of the statements below. The dimension of the eigenspace corresponding to the eigenvalue -4 is necessarily ? ✓ The dimension of the eigenspace corresponding to the eigenvalue -9 is necessarily ? ✓ If the matrix is not diagonalizable, then the dimension of the eigenspace corresponding to the eigenvalue -9 is necessarily ? ✓ If the matrix is symmetric, then the dimension of the eigenspace corresponding to the eigenvalue -9 is necessarily ? ✓

A matrix has characteristic polynomial p(X) = (A + 4) (A + 9)³. Fill in the blanks with the best answer for each of the statements below. The dimension of the eigenspace corresponding to the eigenvalue -4 is necessarily ? ✓ The dimension of the eigenspace corresponding to the eigenvalue -9 is necessarily ? ✓ If the matrix is not diagonalizable, then the dimension of the eigenspace corresponding to the eigenvalue -9 is necessarily ? ✓ If the matrix is symmetric, then the dimension of the eigenspace corresponding to the eigenvalue -9 is necessarily ? ✓

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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A matrix has characteristic polynomial p(X) = (A + 4) (A + 9)³. Fill in the blanks with the best answer for each of the statements below. The dimension of the eigenspace corresponding to the eigenvalue -4 is necessarily ? ✓ The dimension of the eigenspace corresponding to the eigenvalue -9 is necessarily ? ✓ If the matrix is not diagonalizable, then the dimension of the eigenspace corresponding to the eigenvalue -9 is necessarily ? ✓ If the matrix is symmetric, then the dimension of the eigenspace corresponding to the eigenvalue -9 is necessarily ? ✓
Transcribed Image Text:A matrix has characteristic polynomial p(X) = (A + 4) (A + 9)³. Fill in the blanks with the best answer for each of the statements below. The dimension of the eigenspace corresponding to the eigenvalue -4 is necessarily ? ✓ The dimension of the eigenspace corresponding to the eigenvalue -9 is necessarily ? ✓ If the matrix is not diagonalizable, then the dimension of the eigenspace corresponding to the eigenvalue -9 is necessarily ? ✓ If the matrix is symmetric, then the dimension of the eigenspace corresponding to the eigenvalue -9 is necessarily ? ✓
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