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
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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]
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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