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If v1 = and v2 = are eigenvectors of a matrix A corresponding to the eigenvalues A1 = -4 and A2 = -2, respectively,

If v1 = and v2 = are eigenvectors of a matrix A corresponding to the eigenvalues A1 = -4 and A2 = -2, respectively,

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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If \(\mathbf{v}_1 = \begin{bmatrix} -3 \\ 5 \end{bmatrix}\) and \(\mathbf{v}_2 = \begin{bmatrix} -4 \\ 1 \end{bmatrix}\) are eigenvectors of a matrix \(A\) corresponding to the eigenvalues \(\lambda_1 = -4\) and \(\lambda_2 = -2\), respectively,
Transcribed Image Text:If \(\mathbf{v}_1 = \begin{bmatrix} -3 \\ 5 \end{bmatrix}\) and \(\mathbf{v}_2 = \begin{bmatrix} -4 \\ 1 \end{bmatrix}\) are eigenvectors of a matrix \(A\) corresponding to the eigenvalues \(\lambda_1 = -4\) and \(\lambda_2 = -2\), respectively,
The image displays the mathematical expression: \[ \text{and} \, A(3\vec{v}_1) = \begin{bmatrix} \text{[Input Box]} \\ \text{[Input Box]} \end{bmatrix} \] This represents a transformation of the vector \(3\vec{v}_1\) using a matrix \(A\), resulting in a column vector. There are two input boxes provided, indicating where learners can input values for the resulting vector components.
Transcribed Image Text:The image displays the mathematical expression: \[ \text{and} \, A(3\vec{v}_1) = \begin{bmatrix} \text{[Input Box]} \\ \text{[Input Box]} \end{bmatrix} \] This represents a transformation of the vector \(3\vec{v}_1\) using a matrix \(A\), resulting in a column vector. There are two input boxes provided, indicating where learners can input values for the resulting vector components.
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