Let y = orthogonal to u. Q. b. [1] u= write y as the sum of two orthogonal vectors, one in Span {u} and one Co [13] 27 끊][금] 10 10 + 21 9 10 10 [꿀][금 10 39 9 2 2 15 2 45 2
Let y = orthogonal to u. Q. b. [1] u= write y as the sum of two orthogonal vectors, one in Span {u} and one Co [13] 27 끊][금] 10 10 + 21 9 10 10 [꿀][금 10 39 9 2 2 15 2 45 2
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![**Orthogonal Vector Decomposition**
---
Given Problem Statement:
Let \(\mathbf{y} = \begin{bmatrix} 2 \\ 3 \end{bmatrix}\) and \(\mathbf{u} = \begin{bmatrix} 9 \\ 7 \end{bmatrix}\). Write \(\mathbf{y}\) as the sum of two orthogonal vectors, one in \(\text{Span} \{\mathbf{u}\}\) and one orthogonal to \(\mathbf{u}\).
---
**Options:**
**a.**
\[
\begin{bmatrix}
9 \\
-6
\end{bmatrix}
+
\begin{bmatrix}
-7 \\
9
\end{bmatrix}
\]
---
**b.**
\[
\begin{bmatrix}
\frac{27}{10} \\
\frac{21}{10}
\end{bmatrix}
+
\begin{bmatrix}
\frac{7}{10} \\
\frac{9}{10}
\end{bmatrix}
\]
---
**c.**
\[
\begin{bmatrix}
\frac{27}{2} \\
\frac{39}{2}
\end{bmatrix}
+
\begin{bmatrix}
\frac{10}{9} \\
\frac{9}{2}
\end{bmatrix}
\]
---
**d.**
\[
\begin{bmatrix}
-\frac{15}{2} \\
\frac{51}{2}
\end{bmatrix}
+
\begin{bmatrix}
\frac{35}{2} \\
-\frac{45}{2}
\end{bmatrix}
\]
---
**Multiple Choice:**
- \( \circ \) a
- \( \circ \) b
- \( \circ \) c
- \( \circ \) d](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd5246d2a-5796-4784-a543-e596d3b5542c%2Fff7715b0-9ea9-4f74-ae6e-a9793e0bcdf1%2Fboarhm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Orthogonal Vector Decomposition**
---
Given Problem Statement:
Let \(\mathbf{y} = \begin{bmatrix} 2 \\ 3 \end{bmatrix}\) and \(\mathbf{u} = \begin{bmatrix} 9 \\ 7 \end{bmatrix}\). Write \(\mathbf{y}\) as the sum of two orthogonal vectors, one in \(\text{Span} \{\mathbf{u}\}\) and one orthogonal to \(\mathbf{u}\).
---
**Options:**
**a.**
\[
\begin{bmatrix}
9 \\
-6
\end{bmatrix}
+
\begin{bmatrix}
-7 \\
9
\end{bmatrix}
\]
---
**b.**
\[
\begin{bmatrix}
\frac{27}{10} \\
\frac{21}{10}
\end{bmatrix}
+
\begin{bmatrix}
\frac{7}{10} \\
\frac{9}{10}
\end{bmatrix}
\]
---
**c.**
\[
\begin{bmatrix}
\frac{27}{2} \\
\frac{39}{2}
\end{bmatrix}
+
\begin{bmatrix}
\frac{10}{9} \\
\frac{9}{2}
\end{bmatrix}
\]
---
**d.**
\[
\begin{bmatrix}
-\frac{15}{2} \\
\frac{51}{2}
\end{bmatrix}
+
\begin{bmatrix}
\frac{35}{2} \\
-\frac{45}{2}
\end{bmatrix}
\]
---
**Multiple Choice:**
- \( \circ \) a
- \( \circ \) b
- \( \circ \) c
- \( \circ \) d
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