QUESTION 11 Let's try to the Gram-Schmidt process of orthogonalization with the matrix 0.223 0.668 0.710 -0.125 0.741 0.660 0.795 -0.234 0.560 What is the y-coordinate of r3-prime? (don't normalize r3-prime, simply follow the steps, do not use the cross product) Round your answer to 3 decimal places.
QUESTION 11 Let's try to the Gram-Schmidt process of orthogonalization with the matrix 0.223 0.668 0.710 -0.125 0.741 0.660 0.795 -0.234 0.560 What is the y-coordinate of r3-prime? (don't normalize r3-prime, simply follow the steps, do not use the cross product) Round your answer to 3 decimal places.
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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please answer the following question with the formula listed
![**Question 11:**
Let's try the Gram-Schmidt process of orthogonalization with the matrix:
\[
\begin{bmatrix}
0.223 & 0.668 & 0.710 \\
-0.125 & 0.741 & 0.660 \\
0.795 & -0.234 & 0.560 \\
\end{bmatrix}
\]
What is the y-coordinate of r3-prime? (Don't normalize r3-prime, simply follow the steps, do not use the cross product)
Round your answer to 3 decimal places.
[Answer box]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc8ef3851-b223-4be3-ac39-739e48c0c7a3%2Fb76e1d24-3b15-413b-9bae-42e0844cea36%2Fm53n184_processed.png&w=3840&q=75)
Transcribed Image Text:**Question 11:**
Let's try the Gram-Schmidt process of orthogonalization with the matrix:
\[
\begin{bmatrix}
0.223 & 0.668 & 0.710 \\
-0.125 & 0.741 & 0.660 \\
0.795 & -0.234 & 0.560 \\
\end{bmatrix}
\]
What is the y-coordinate of r3-prime? (Don't normalize r3-prime, simply follow the steps, do not use the cross product)
Round your answer to 3 decimal places.
[Answer box]

Transcribed Image Text:The text in the image appears to be a series of vector equations used in mathematics, possibly in the context of numerical methods or linear algebra. The equations are as follows:
1. \( \mathbf{r}_1' \gets \mathbf{r}_1 \),
2. \( \mathbf{r}_2' \gets \mathbf{r}_2 - \frac{\mathbf{r}_2 \cdot \mathbf{r}_1'}{\mathbf{r}_1' \cdot \mathbf{r}_1'} \mathbf{r}_1' \),
3. \( \mathbf{r}_3' \gets \mathbf{r}_3 - \frac{\mathbf{r}_3 \cdot \mathbf{r}_1'}{\mathbf{r}_1' \cdot \mathbf{r}_1'} \mathbf{r}_1' - \frac{\mathbf{r}_3 \cdot \mathbf{r}_2'}{\mathbf{r}_2' \cdot \mathbf{r}_2'} \mathbf{r}_2' \).
Explanation:
- These equations appear to describe a process of vector orthogonalization, possibly using the Gram-Schmidt process.
- \( \mathbf{r}_1' \) is initialized as \( \mathbf{r}_1 \).
- \( \mathbf{r}_2' \) is obtained by projecting \( \mathbf{r}_2 \) onto \( \mathbf{r}_1' \) and then subtracting this projection from \( \mathbf{r}_2 \), ensuring \( \mathbf{r}_2' \) is orthogonal to \( \mathbf{r}_1' \).
- \( \mathbf{r}_3' \) is computed similarly by orthogonalizing \( \mathbf{r}_3 \) with respect to both \( \mathbf{r}_1' \) and \( \mathbf{r}_2' \), ensuring it is orthogonal to both.
These steps are fundamental in creating an orthogonal set of vectors from a linearly independent set.
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