B = 2 1 -1 2 -1 3 -1 2 -2
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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Question
One can check that λ = 5, 1 are eigenvalues of B.
If possible, diagonalize matrix B or explain why B is not diagonalizable.
![The matrix \( B \) is given as:
\[
B = \begin{bmatrix}
2 & 2 & -1 \\
1 & 3 & -1 \\
-1 & -2 & 2
\end{bmatrix}.
\]
This matrix \( B \) is a 3x3 matrix, which means it has 3 rows and 3 columns. Each entry in the matrix is a real number, and they are arranged in a specific order as shown.
In this matrix:
- The first row is \([2, 2, -1]\),
- The second row is \([1, 3, -1]\),
- The third row is \([-1, -2, 2]\).
Matrices like this are used in various areas of mathematics and applied sciences, such as solving systems of linear equations, transformations in geometry, and more.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9612546f-987e-4906-abd4-8f6ba2df88e4%2F56eb3597-0533-48e2-bd4d-a6d30170d2ea%2Fd1l5rce_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The matrix \( B \) is given as:
\[
B = \begin{bmatrix}
2 & 2 & -1 \\
1 & 3 & -1 \\
-1 & -2 & 2
\end{bmatrix}.
\]
This matrix \( B \) is a 3x3 matrix, which means it has 3 rows and 3 columns. Each entry in the matrix is a real number, and they are arranged in a specific order as shown.
In this matrix:
- The first row is \([2, 2, -1]\),
- The second row is \([1, 3, -1]\),
- The third row is \([-1, -2, 2]\).
Matrices like this are used in various areas of mathematics and applied sciences, such as solving systems of linear equations, transformations in geometry, and more.
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