**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

Answered: Image /qna-images/answer/d570cdb6-62f9-4394-be5c-cf09ef5d8fc8.jpg

Answered: 24 --[:] A= 36 (1) Det(A) is 0, so the…

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

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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

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