Question

Let \[ A=\left[\begin{array}{ccc} -1 & 0 & 0 \\ -8 & -1 & -4 \\ 6 & 2 & 5 \end{array}\right] . \] If possible, find an invertible matrix \( P \) so that \( D=P^{-1} A P \) is a diagonal matrix. If it is not possible, enter the identity matrix for \( P \) and the matrix \( A \) for \( D \). You must enter a number in every answer blank for the answer evaluator to work properly. Is \( A \) diagonalizable over \( \mathbb{R} \) ? choose \( \square \) Be sure you can explain why or why not.

          Let
\[
A=\left[\begin{array}{ccc}
-1 & 0 & 0 \\
-8 & -1 & -4 \\
6 & 2 & 5
\end{array}\right] .
\]

If possible, find an invertible matrix \( P \) so that \( D=P^{-1} A P \) is a diagonal matrix. If it is not possible, enter the identity matrix for \( P \) and the matrix \( A \) for \( D \). You must enter a number in every answer blank for the answer evaluator to work properly.

Is \( A \) diagonalizable over \( \mathbb{R} \) ? choose \( \square \) Be sure you can explain why or why not.

Show more…

Let

A=[
-1 0 0

-8 -1 -4

6 2 5
] .

If possible, find an invertible matrix P so that D=P^-1 A P is a diagonal matrix. If it is not possible, enter the identity matrix for P and the matrix A for D. You must enter a number in every answer blank for the answer evaluator to work properly.

Is A diagonalizable over ℝ ? choose □ Be sure you can explain why or why not.

Added by Emilio C.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert William F

Step 1

The characteristic polynomial is given by \( \det(A - \lambda I) \), where \( I \) is the identity matrix. \[ A - \lambda I = \begin{bmatrix} -1-\lambda & 0 & 0 \\ -8 & -1-\lambda & -4 \\ 6 & 2 & 5-\lambda \end{bmatrix} \] Calculate the determinant: \[ \det(A Show more…

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Let \[ A=\left[\begin{array}{ccc} -1 & 0 & 0 \\ -8 & -1 & -4 \\ 6 & 2 & 5 \end{array}\right] . \] If possible, find an invertible matrix \( P \) so that \( D=P^{-1} A P \) is a diagonal matrix. If it is not possible, enter the identity matrix for \( P \) and the matrix \( A \) for \( D \). You must enter a number in every answer blank for the answer evaluator to work properly. Is \( A \) diagonalizable over \( \mathbb{R} \) ? choose \( \square \) Be sure you can explain why or why not.

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