Advanced Engineering Mathematics
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ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![For the matrix \( A \), find (if possible) a nonsingular matrix \( P \) such that \( P^{-1}AP \) is diagonal. (If not possible, enter IMPOSSIBLE.)
\[ A = \begin{bmatrix} 1 & \frac{1}{2} \\ -\frac{3}{2} & -1 \end{bmatrix} \]
\[ P = \begin{bmatrix} \square & \square \\ \square & \square \end{bmatrix} \]
Verify that \( P^{-1}AP \) is a diagonal matrix with the eigenvalues on the main diagonal.
\[ P^{-1}AP = \begin{bmatrix} \square & \square \\ \square & \square \end{bmatrix} \]](https://content.bartleby.com/qna-images/question/61ff295b-afd4-43c3-8ed2-2cc17b9c2249/b22f3371-f2e1-47de-9ad6-b87c44f1fbc1/6nb9aog_processed.png)
Transcribed Image Text:For the matrix \( A \), find (if possible) a nonsingular matrix \( P \) such that \( P^{-1}AP \) is diagonal. (If not possible, enter IMPOSSIBLE.)
\[ A = \begin{bmatrix} 1 & \frac{1}{2} \\ -\frac{3}{2} & -1 \end{bmatrix} \]
\[ P = \begin{bmatrix} \square & \square \\ \square & \square \end{bmatrix} \]
Verify that \( P^{-1}AP \) is a diagonal matrix with the eigenvalues on the main diagonal.
\[ P^{-1}AP = \begin{bmatrix} \square & \square \\ \square & \square \end{bmatrix} \]
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