Which of the following statements is/are true regarding the matrix A? 3 -51 0. A = -4 A) The columns of A form a basis of R B) Nul A = {0} C) dim Nul A=1 D) rank A = 3 O a. D O b. B and C O c. None of the answers is correct O d. C O e. A and B O f. Cand D O g. A O h. B
Which of the following statements is/are true regarding the matrix A? 3 -51 0. A = -4 A) The columns of A form a basis of R B) Nul A = {0} C) dim Nul A=1 D) rank A = 3 O a. D O b. B and C O c. None of the answers is correct O d. C O e. A and B O f. Cand D O g. A O h. B
Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Matrix A and Related Statements
Consider the matrix \(A\) given below:
\[ A = \begin{bmatrix}
0 & 3 & -5 \\
1 & 0 & 2 \\
-4 & -9 & 7
\end{bmatrix} \]
Which of the following statements is/are true regarding the matrix \(A\)?
### Statements:
- **A)** The columns of \(A\) form a basis of \(\mathbb{R}^n\).
- **B)** \( \text{Nul }A = \{0\} \)
- **C)** \(\dim \text{Nul } A = 1\)
- **D)** \( \text{rank } A = 3 \)
### Options:
- **a.** \( \text{A and D} \)
- **b.** \( \text{B and C} \)
- **c.** \( \text{None of the answers is correct} \)
- **d.** \( \text{C} \)
- **e.** \( \text{A and B} \)
- **f.** \( \text{C and D} \)
- **g.** \( \text{A} \)
- **h.** \( \text{B} \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F039f7f42-bea1-420c-8e74-506e9aacc740%2Fde44c69f-0236-4af7-a208-1b51f95d4339%2Fxyww8j9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Matrix A and Related Statements
Consider the matrix \(A\) given below:
\[ A = \begin{bmatrix}
0 & 3 & -5 \\
1 & 0 & 2 \\
-4 & -9 & 7
\end{bmatrix} \]
Which of the following statements is/are true regarding the matrix \(A\)?
### Statements:
- **A)** The columns of \(A\) form a basis of \(\mathbb{R}^n\).
- **B)** \( \text{Nul }A = \{0\} \)
- **C)** \(\dim \text{Nul } A = 1\)
- **D)** \( \text{rank } A = 3 \)
### Options:
- **a.** \( \text{A and D} \)
- **b.** \( \text{B and C} \)
- **c.** \( \text{None of the answers is correct} \)
- **d.** \( \text{C} \)
- **e.** \( \text{A and B} \)
- **f.** \( \text{C and D} \)
- **g.** \( \text{A} \)
- **h.** \( \text{B} \)
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