Find a 2x2 matrix A that has two eigenvalues 4, -1 whose eigenvectors -3 and -1 1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Find a \(2 \times 2\) matrix \(A\) that has two eigenvalues \(4, -1\) whose eigenvectors are \(\begin{bmatrix} 2 \\ 1 \end{bmatrix}\) and \(\begin{bmatrix} -3 \\ -1 \end{bmatrix}\).
Transcribed Image Text:Find a \(2 \times 2\) matrix \(A\) that has two eigenvalues \(4, -1\) whose eigenvectors are \(\begin{bmatrix} 2 \\ 1 \end{bmatrix}\) and \(\begin{bmatrix} -3 \\ -1 \end{bmatrix}\).
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