Find an orthogonal set with the same span (and same number of elements) as 9 27 12 4 11 21 -10 -91 4 -5 13 -36
Find an orthogonal set with the same span (and same number of elements) as 9 27 12 4 11 21 -10 -91 4 -5 13 -36
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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![**Task: Orthogonal Set with the Same Span**
Find an orthogonal set with the same span (and same number of elements) as the following vectors:
Given Set:
\[
\left\{
\begin{bmatrix}
9 \\
12 \\
11 \\
-10
\end{bmatrix},
\begin{bmatrix}
-9 \\
4 \\
-5 \\
13
\end{bmatrix},
\begin{bmatrix}
27 \\
4 \\
21 \\
-36
\end{bmatrix}
\right\}
\]
Objective: Determine an orthogonal set of vectors that maintains the span and number of elements from the given set. The resulting orthogonal vectors are represented as blank column matrices, indicating where the solution will be filled in:
Expected Orthogonal Set:
\[
\left\{
\begin{bmatrix}
\boxed{\phantom{0}} \\
\boxed{\phantom{0}} \\
\boxed{\phantom{0}} \\
\boxed{\phantom{0}}
\end{bmatrix},
\begin{bmatrix}
\boxed{\phantom{0}} \\
\boxed{\phantom{0}} \\
\boxed{\phantom{0}} \\
\boxed{\phantom{0}}
\end{bmatrix},
\begin{bmatrix}
\boxed{\phantom{0}} \\
\boxed{\phantom{0}} \\
\boxed{\phantom{0}} \\
\boxed{\phantom{0}}
\end{bmatrix}
\right\}
\]
Use the Gram-Schmidt process or another orthogonalization method to find the orthogonal vectors. Each box represents a component of the orthogonal vectors to be calculated.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F807728d5-81cc-4dac-b6a1-9785980c085b%2F2c79355d-3331-4003-ab8f-10d436d47670%2F5ii4kfa_processed.png&w=3840&q=75)
Transcribed Image Text:**Task: Orthogonal Set with the Same Span**
Find an orthogonal set with the same span (and same number of elements) as the following vectors:
Given Set:
\[
\left\{
\begin{bmatrix}
9 \\
12 \\
11 \\
-10
\end{bmatrix},
\begin{bmatrix}
-9 \\
4 \\
-5 \\
13
\end{bmatrix},
\begin{bmatrix}
27 \\
4 \\
21 \\
-36
\end{bmatrix}
\right\}
\]
Objective: Determine an orthogonal set of vectors that maintains the span and number of elements from the given set. The resulting orthogonal vectors are represented as blank column matrices, indicating where the solution will be filled in:
Expected Orthogonal Set:
\[
\left\{
\begin{bmatrix}
\boxed{\phantom{0}} \\
\boxed{\phantom{0}} \\
\boxed{\phantom{0}} \\
\boxed{\phantom{0}}
\end{bmatrix},
\begin{bmatrix}
\boxed{\phantom{0}} \\
\boxed{\phantom{0}} \\
\boxed{\phantom{0}} \\
\boxed{\phantom{0}}
\end{bmatrix},
\begin{bmatrix}
\boxed{\phantom{0}} \\
\boxed{\phantom{0}} \\
\boxed{\phantom{0}} \\
\boxed{\phantom{0}}
\end{bmatrix}
\right\}
\]
Use the Gram-Schmidt process or another orthogonalization method to find the orthogonal vectors. Each box represents a component of the orthogonal vectors to be calculated.
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