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Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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
Transcribed Image Text:Find the eigenvalues of the matrix and determine whether there is a sufficient number to guarantee that the matrix is diagonalizable. (Recall that the matrix may be diagonalizable even though it is not guaranteed to be
diagonalizable by the theorem shown below.)
Sufficient Condition for Diagonalization
If an n x n matrix A has n distinct eigenvalues, then the corresponding eigenvectors are linearly independent and A is diagonalizable.
-3 3 -1
0-2 5
0 0 2
Find the eigenvalues. (Enter your answers as a comma-separated list.)
λ =
Is there a sufficient number to guarantee that the matrix is diagonalizable?
O Yes
O No
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- Show that is an eigenvalue of the matrix and determine a basis for its eigenspace. 5 3 9 97 3 5 9, λ=2 -3-3-7arrow_forwardSelect T if the statement is true (in all cases), or select F if false (for at least one example).arrow_forwardLet A be an nxn matrix. Determine whether the statement below is true or false. Justify the answer. The multiplicity of a root r of the characteristic equation of A is called the algebraic multiplicity of r as an eigenvalue of A. The statement is false. The multiplicity of a root r of the characteristic equation of A is the number of eigenvectors corresponding to that root. The statement is true. It is the definition of the multiplicity of a root of the characteristic equation of A. The statement is true. It is the definition of the algebraic multiplicity of an eigenvalue of A. OThe statement is false. The multiplicity of a rootr of the characteristic equation. of A is called the geometric multiplicity of r as an eigenvalue of A.arrow_forward
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