Find ordhogonal bor each ob the bollowing. unitary dagoralizeng an OY matrix
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
Find an orthogonal or unitary diagonalizing matrix for each of the following:
(a) \[
\begin{bmatrix}
2 & 1 \\
1 & 2
\end{bmatrix}
\]
(b) \[
\begin{bmatrix}
1 & 3+i \\
3-i & 4
\end{bmatrix}
\]
(c) \[
\begin{bmatrix}
2 & i & 0 \\
-i & 2 & 0 \\
0 & 0 & 2
\end{bmatrix}
\]
(d) \[
\begin{bmatrix}
2 & 1 & 1 \\
1 & 3 & -2 \\
1 & -2 & 3
\end{bmatrix}
\]
(e) \[
\begin{bmatrix}
0 & 0 & 1 \\
0 & 1 & 0 \\
1 & 0 & 0
\end{bmatrix}
\]
(f) \[
\begin{bmatrix}
1 & 1 & 1 \\
1 & 1 & 1 \\
1 & 1 & 1
\end{bmatrix}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3fdbb1a7-d573-479c-8d2a-d1c6b6fb9ae3%2F122932cc-75d9-486d-86e1-ce25e1a32659%2Fgen67sf_processed.png&w=3840&q=75)
Transcribed Image Text:### Question
Find an orthogonal or unitary diagonalizing matrix for each of the following:
(a) \[
\begin{bmatrix}
2 & 1 \\
1 & 2
\end{bmatrix}
\]
(b) \[
\begin{bmatrix}
1 & 3+i \\
3-i & 4
\end{bmatrix}
\]
(c) \[
\begin{bmatrix}
2 & i & 0 \\
-i & 2 & 0 \\
0 & 0 & 2
\end{bmatrix}
\]
(d) \[
\begin{bmatrix}
2 & 1 & 1 \\
1 & 3 & -2 \\
1 & -2 & 3
\end{bmatrix}
\]
(e) \[
\begin{bmatrix}
0 & 0 & 1 \\
0 & 1 & 0 \\
1 & 0 & 0
\end{bmatrix}
\]
(f) \[
\begin{bmatrix}
1 & 1 & 1 \\
1 & 1 & 1 \\
1 & 1 & 1
\end{bmatrix}
\]
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