24 --[:] A= 36 (1) Det(A) is 0, so the inverse of A does not exist. (2) Det(A) is 0, so the Adjoint of A does not exist. (3)Det(A) is 0, so the transpose of A does not exist. Which one is true?
24 --[:] A= 36 (1) Det(A) is 0, so the inverse of A does not exist. (2) Det(A) is 0, so the Adjoint of A does not exist. (3)Det(A) is 0, so the transpose of A does not exist. Which one is true?
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
![**Matrix A and Determinant Discussion**
Matrix A is given by:
\[ A = \begin{bmatrix} 2 & 4 \\ 3 & 6 \end{bmatrix} \]
Consider the following statements:
1. Det(A) is 0, so the inverse of A does not exist.
2. Det(A) is 0, so the Adjoint of A does not exist.
3. Det(A) is 0, so the transpose of A does not exist.
The question asks: Which one is true?
**Options:**
- (1) AND (2)
- (2) AND (3)
- (2) ONLY
- (1) ONLY
**Explanation:**
- **Statement 1**: If the determinant of A (Det(A)) is 0, the matrix is singular, and hence its inverse does not exist. This is true.
- **Statement 2**: The adjoint of a matrix always exists regardless of whether the determinant is zero. This is false.
- **Statement 3**: The transpose of a matrix always exists regardless of the determinant. This is false.
Thus, only statement (1) is true, so the correct choice is:
- (1) ONLY](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac0f3c56-5561-4b47-8ddf-f02546f51c3e%2Fd570cdb6-62f9-4394-be5c-cf09ef5d8fc8%2Fqn8ezd_processed.png&w=3840&q=75)
Transcribed Image Text:**Matrix A and Determinant Discussion**
Matrix A is given by:
\[ A = \begin{bmatrix} 2 & 4 \\ 3 & 6 \end{bmatrix} \]
Consider the following statements:
1. Det(A) is 0, so the inverse of A does not exist.
2. Det(A) is 0, so the Adjoint of A does not exist.
3. Det(A) is 0, so the transpose of A does not exist.
The question asks: Which one is true?
**Options:**
- (1) AND (2)
- (2) AND (3)
- (2) ONLY
- (1) ONLY
**Explanation:**
- **Statement 1**: If the determinant of A (Det(A)) is 0, the matrix is singular, and hence its inverse does not exist. This is true.
- **Statement 2**: The adjoint of a matrix always exists regardless of whether the determinant is zero. This is false.
- **Statement 3**: The transpose of a matrix always exists regardless of the determinant. This is false.
Thus, only statement (1) is true, so the correct choice is:
- (1) ONLY
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
