Give the rank and the nullity of the matrix. 20 -2 A = rank(A) = nullity(A) =
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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![### Exercise 1: POOLLEINALG4 3.5.035
**Problem:**
- Determine the rank and the nullity of the matrix \( A \).
**Matrix:**
\[ A = \begin{bmatrix} 2 & 0 & -2 \\ 1 & 1 & 1 \end{bmatrix} \]
- **Find:**
- Rank\( A \) = ___
- Nullity\( A \) = ___
**Additional Resources:**
- Need Help? [Read It]
---
### Exercise 2: POOLLEINALG4 3.5.042
**Problem:**
- If \( A \) is a 4 x 2 matrix, what are the possible values of nullity\( A \)?
- **Note:** Enter your answers as a comma-separated list.
**Find:**
- Nullity\( A \) = ___
**Additional Resources:**
- Need Help? [Read It]
---
### Exercise 3: POOLLEINALG4 3.5.041
**Problem:**
- If \( A \) is a 3 x 5 matrix, what are the possible values of nullity\( A \)?
- **Note:** Enter your answers as a comma-separated list.
**Find:**
- Nullity\( A \) = ___
**Additional Resources:**
- Need Help? [Read It]
---
### Exercise 4: POOLLEINALG4 3.5.044
**Problem:**
- Find all possible values of rank\( A \) as \( a \) varies.
- **Note:** Enter your answers as a comma-separated list.
**Matrix:**
\[ A = \begin{bmatrix} a & 2 & -1 \\ 3 & 3 & -2 \\ -2 & -1 & a \end{bmatrix} \]
- **Find:**
- Rank\( A \) = ___
**Additional Resources:**
- Need Help? [Read It]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6d702b96-16c9-42c6-953e-90c469a3b56f%2Fd1fef8ec-1fcc-427f-9f44-5c903b90a9e3%2F6moccb_processed.png&w=3840&q=75)
Transcribed Image Text:### Exercise 1: POOLLEINALG4 3.5.035
**Problem:**
- Determine the rank and the nullity of the matrix \( A \).
**Matrix:**
\[ A = \begin{bmatrix} 2 & 0 & -2 \\ 1 & 1 & 1 \end{bmatrix} \]
- **Find:**
- Rank\( A \) = ___
- Nullity\( A \) = ___
**Additional Resources:**
- Need Help? [Read It]
---
### Exercise 2: POOLLEINALG4 3.5.042
**Problem:**
- If \( A \) is a 4 x 2 matrix, what are the possible values of nullity\( A \)?
- **Note:** Enter your answers as a comma-separated list.
**Find:**
- Nullity\( A \) = ___
**Additional Resources:**
- Need Help? [Read It]
---
### Exercise 3: POOLLEINALG4 3.5.041
**Problem:**
- If \( A \) is a 3 x 5 matrix, what are the possible values of nullity\( A \)?
- **Note:** Enter your answers as a comma-separated list.
**Find:**
- Nullity\( A \) = ___
**Additional Resources:**
- Need Help? [Read It]
---
### Exercise 4: POOLLEINALG4 3.5.044
**Problem:**
- Find all possible values of rank\( A \) as \( a \) varies.
- **Note:** Enter your answers as a comma-separated list.
**Matrix:**
\[ A = \begin{bmatrix} a & 2 & -1 \\ 3 & 3 & -2 \\ -2 & -1 & a \end{bmatrix} \]
- **Find:**
- Rank\( A \) = ___
**Additional Resources:**
- Need Help? [Read It]
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