Determine if X = -3 is an eigenvalue of the matrix A = V 2 6 -12 0 0 -9-4 24 11
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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![**Determine if \(\lambda = -3\) is an eigenvalue of the matrix \( A \):**
\[
A = \begin{bmatrix}
2 & 0 & 0 \\
6 & -9 & -4 \\
-12 & 24 & 11
\end{bmatrix}
\]
In this problem, we are tasked with determining whether the scalar \(\lambda = -3\) is an eigenvalue of the matrix \( A \). An eigenvalue of a matrix is a number such that there exists a non-zero vector \(\mathbf{v}\) which satisfies the equation \( A\mathbf{v} = \lambda\mathbf{v} \).
To verify, one must check whether the determinant of the matrix \( (A - \lambda I) \) is zero, where \( I \) is the identity matrix.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18574973-f25e-4ab8-b7d6-6007b5b87fc4%2F2b766c5b-bd29-4b60-9424-e8e67bcfef7a%2Fnbp0hso_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Determine if \(\lambda = -3\) is an eigenvalue of the matrix \( A \):**
\[
A = \begin{bmatrix}
2 & 0 & 0 \\
6 & -9 & -4 \\
-12 & 24 & 11
\end{bmatrix}
\]
In this problem, we are tasked with determining whether the scalar \(\lambda = -3\) is an eigenvalue of the matrix \( A \). An eigenvalue of a matrix is a number such that there exists a non-zero vector \(\mathbf{v}\) which satisfies the equation \( A\mathbf{v} = \lambda\mathbf{v} \).
To verify, one must check whether the determinant of the matrix \( (A - \lambda I) \) is zero, where \( I \) is the identity matrix.
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