Find Q for the QR factorization of A Q = Ex: 1.23 1 V2 1 0 -2 -2 [9] 0 2 -10 0 -5 -3 -10, V3 = 0.38 -0.1 0.19 , given the orthogonal vectors
Find Q for the QR factorization of A Q = Ex: 1.23 1 V2 1 0 -2 -2 [9] 0 2 -10 0 -5 -3 -10, V3 = 0.38 -0.1 0.19 , given the orthogonal vectors
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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![### QR Factorization Problem
#### Problem Statement:
Find \( Q \) for the \( QR \) factorization of \( A \) given the orthogonal vectors.
#### Given Matrix:
\[ A = \begin{bmatrix}
1 & 0 & 2 \\
0 & -10 & 0 \\
-2 & -5 & -3
\end{bmatrix} \]
#### Orthogonal Vectors:
\[ \mathbf{v}_1 = \begin{bmatrix}
1 \\
0 \\
-2
\end{bmatrix}, \quad
\mathbf{v}_2 = \begin{bmatrix}
-2 \\
-10 \\
-1
\end{bmatrix}, \quad
\mathbf{v}_3 = \begin{bmatrix}
0.38 \\
-0.1 \\
0.19
\end{bmatrix} \]
#### Matrix \( Q \):
\[ Q = \begin{bmatrix}
\text{Ex: 1.23} & & \\
& & \\
& &
\end{bmatrix} \]
You are provided with the orthogonal vectors \(\mathbf{v}_1 , \mathbf{v}_2 , \mathbf{v}_3 \). Use them to construct the orthogonal matrix \( Q \) for the \( QR \) factorization of the given matrix \( A \).
Enter the values in the blank spaces provided for matrix \( Q \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf8aa82a-31a1-4382-a30e-3ad6a3174f84%2F24abb9b2-1aad-44ff-b53f-fac7d84208ea%2Fctj561j_processed.png&w=3840&q=75)
Transcribed Image Text:### QR Factorization Problem
#### Problem Statement:
Find \( Q \) for the \( QR \) factorization of \( A \) given the orthogonal vectors.
#### Given Matrix:
\[ A = \begin{bmatrix}
1 & 0 & 2 \\
0 & -10 & 0 \\
-2 & -5 & -3
\end{bmatrix} \]
#### Orthogonal Vectors:
\[ \mathbf{v}_1 = \begin{bmatrix}
1 \\
0 \\
-2
\end{bmatrix}, \quad
\mathbf{v}_2 = \begin{bmatrix}
-2 \\
-10 \\
-1
\end{bmatrix}, \quad
\mathbf{v}_3 = \begin{bmatrix}
0.38 \\
-0.1 \\
0.19
\end{bmatrix} \]
#### Matrix \( Q \):
\[ Q = \begin{bmatrix}
\text{Ex: 1.23} & & \\
& & \\
& &
\end{bmatrix} \]
You are provided with the orthogonal vectors \(\mathbf{v}_1 , \mathbf{v}_2 , \mathbf{v}_3 \). Use them to construct the orthogonal matrix \( Q \) for the \( QR \) factorization of the given matrix \( A \).
Enter the values in the blank spaces provided for matrix \( Q \).
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