Show that the matrix is not diagonalizable. 3-4 1 3 1 04 0 0 STEP 1: Use the fact that the matrix is triangular to write down the eigenvalues. (Enter your answers from smallest to largest.) (2₁, 2₂) =) STEP 2: Find the eigenvectors X₁ and x₂ corresponding to ₁ and 2₂, respectively. X₁ = x2 = STEP 3: Since the matrix does not have. ---Select--- linearly independent eigenvectors, you can conclude that the matrix is not diagonalizable.
Show that the matrix is not diagonalizable. 3-4 1 3 1 04 0 0 STEP 1: Use the fact that the matrix is triangular to write down the eigenvalues. (Enter your answers from smallest to largest.) (2₁, 2₂) =) STEP 2: Find the eigenvectors X₁ and x₂ corresponding to ₁ and 2₂, respectively. X₁ = x2 = STEP 3: Since the matrix does not have. ---Select--- linearly independent eigenvectors, you can conclude that the matrix is not diagonalizable.
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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![Show that the matrix is not diagonalizable.
\[
\begin{bmatrix}
3 & -4 & 1 \\
0 & 3 & 1 \\
0 & 0 & 4
\end{bmatrix}
\]
**STEP 1:** Use the fact that the matrix is triangular to write down the eigenvalues. (Enter your answers from smallest to largest.)
\[
(\lambda_1, \lambda_2) = ( \_\_\_\_ , \_\_\_\_ )
\]
**STEP 2:** Find the eigenvectors \(\mathbf{x_1}\) and \(\mathbf{x_2}\) corresponding to \(\lambda_1\) and \(\lambda_2\), respectively.
\[
\mathbf{x_1} = \begin{bmatrix} \_\_ \\ \_\_ \\ \_\_ \end{bmatrix}
\]
\[
\mathbf{x_2} = \begin{bmatrix} \_\_ \\ \_\_ \\ \_\_ \end{bmatrix}
\]
**STEP 3:** Since the matrix does not have [Select] linearly independent eigenvectors, you can conclude that the matrix is not diagonalizable.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F61ff295b-afd4-43c3-8ed2-2cc17b9c2249%2F9d9a6579-1f78-498f-8012-9c03462d336e%2Fw7d368x_processed.png&w=3840&q=75)
Transcribed Image Text:Show that the matrix is not diagonalizable.
\[
\begin{bmatrix}
3 & -4 & 1 \\
0 & 3 & 1 \\
0 & 0 & 4
\end{bmatrix}
\]
**STEP 1:** Use the fact that the matrix is triangular to write down the eigenvalues. (Enter your answers from smallest to largest.)
\[
(\lambda_1, \lambda_2) = ( \_\_\_\_ , \_\_\_\_ )
\]
**STEP 2:** Find the eigenvectors \(\mathbf{x_1}\) and \(\mathbf{x_2}\) corresponding to \(\lambda_1\) and \(\lambda_2\), respectively.
\[
\mathbf{x_1} = \begin{bmatrix} \_\_ \\ \_\_ \\ \_\_ \end{bmatrix}
\]
\[
\mathbf{x_2} = \begin{bmatrix} \_\_ \\ \_\_ \\ \_\_ \end{bmatrix}
\]
**STEP 3:** Since the matrix does not have [Select] linearly independent eigenvectors, you can conclude that the matrix is not diagonalizable.
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