(0, -1, -3)
(0, -2, -3)
(0, 2, 3)
(0, 1, 3)
Answer is Right!
Answer is Wrong!
The correct answer is $\boxed{\text{(0, -1, -3)}}$.
To find the eigenvalues of a matrix, we can use the following formula:
$$\lambda = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}$$
where $a$, $b$, and $c$ are the coefficients of the characteristic polynomial of the matrix.
The characteristic polynomial of the matrix $A$ is given by:
$$p(x) = |A – xI| = x^3 – 4x^2 + 3x – 0$$
To find the eigenvalues of $A$, we need to solve the equation $p(x) = 0$.
Solving $p(x) = 0$, we get the following eigenvalues:
$$\lambda = 0, -1, -3$$
Therefore, the eigenvalues of the matrix $A$ are $\boxed{\text{(0, -1, -3)}}$.
Here is a brief explanation of each option:
- Option A: $(0, -1, -3)$. This is the correct answer.
- Option B: $(0, -2, -3)$. This is not the correct answer because the eigenvalue $-2$ is not an eigenvalue of the matrix $A$.
- Option C: $(0, 2, 3)$. This is not the correct answer because the eigenvalue $2$ is not an eigenvalue of the matrix $A$.
- Option D: $(0, 1, 3)$. This is not the correct answer because the eigenvalue $1$ is not an eigenvalue of the matrix $A$.