1 -2 2 1 5 2 -2 0-2 1 -1 1 2 The orthogonal complement of the column space of A is the span of the set ((-2,2,3,0)) Let A = a. b. ((-2,2,3,1),(-1,0,0,1)) {(2,2,3,0), (-1,0,0,1)) d. ((-2,2,3,0), (-1,0,0,1)) e. ((-2,2,3,0), (1,0,0,1)) O a Ob OC O -1 1 2 1 d
1 -2 2 1 5 2 -2 0-2 1 -1 1 2 The orthogonal complement of the column space of A is the span of the set ((-2,2,3,0)) Let A = a. b. ((-2,2,3,1),(-1,0,0,1)) {(2,2,3,0), (-1,0,0,1)) d. ((-2,2,3,0), (-1,0,0,1)) e. ((-2,2,3,0), (1,0,0,1)) O a Ob OC O -1 1 2 1 d
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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![### Orthogonal Complement of the Column Space
Given the matrix \( A \):
\[ A = \begin{bmatrix}
1 & -1 & 1 & 2 \\
-2 & 2 & 1 & 5 \\
2 & -2 & 0 & -2 \\
1 & -1 & 1 & 2 \\
\end{bmatrix} \]
We need to determine the orthogonal complement of the column space of \( A \).
The orthogonal complement of the column space of \( A \) is the span of the set:
**Options:**
- **a.** \( \{(-2, 2, 3, 0)\} \)
- **b.** \( \{(-2, 2, 3, 1), (-1, 0, 0, 1)\} \)
- **c.** \( \{(2, 2, 3, 0), (-1, 0, 0, 1)\} \)
- **d.** \( \{(-2, 2, 3, 0), (-1, 0, 0, 1)\} \)
- **e.** \( \{(-2, 2, 3, 0), (1, 0, 0, 1)\} \)
**Select the correct answer:**
- ⭕ a
- ⭕ b
- ⭕ c
- ⭕ d
- ⭕ e](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd5246d2a-5796-4784-a543-e596d3b5542c%2Fa5c23e24-b9fe-4be8-8833-653030aee3d8%2F40wo8g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Orthogonal Complement of the Column Space
Given the matrix \( A \):
\[ A = \begin{bmatrix}
1 & -1 & 1 & 2 \\
-2 & 2 & 1 & 5 \\
2 & -2 & 0 & -2 \\
1 & -1 & 1 & 2 \\
\end{bmatrix} \]
We need to determine the orthogonal complement of the column space of \( A \).
The orthogonal complement of the column space of \( A \) is the span of the set:
**Options:**
- **a.** \( \{(-2, 2, 3, 0)\} \)
- **b.** \( \{(-2, 2, 3, 1), (-1, 0, 0, 1)\} \)
- **c.** \( \{(2, 2, 3, 0), (-1, 0, 0, 1)\} \)
- **d.** \( \{(-2, 2, 3, 0), (-1, 0, 0, 1)\} \)
- **e.** \( \{(-2, 2, 3, 0), (1, 0, 0, 1)\} \)
**Select the correct answer:**
- ⭕ a
- ⭕ b
- ⭕ c
- ⭕ d
- ⭕ e
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