Word Count : 959

---

### Problem 1: Diagonalizability of Matrix A Given matrix \( A \): \[ A = \begin{bmatrix} 0 & 1 & -3 \\ 2 & -1 & 6 \\ 1 & -1 & 4 \end{bmatrix} \] #### Step 1: Find the eigenvalues of \( A \) To check if \( A \) is diagonalizable, we first need to find its eigenvalues by solving the characteristic equation: \[ \text{det}(A - \lambda I) = 0 \] Where \( I \) is the identity matrix and \( \lambda \) represents the eigenvalue. \[ A - \lambda I = \begin{bmatrix} 0 - \lambda & 1 & -3 \\ 2 & -1 - \lambda & 6 \\ 1 & -1 & 4 - \lambda \end{bmatrix} \] The determinant of \( A - \lambda I \) is: \[ \text{det}(A - \lambda I) = \text{det}\begin{bmatrix} -\lambda & 1 & -3 \\ 2 & -1-\lambda & 6 \\ 1 & -1 & 4-\lambda \end{bmatrix} \] Expanding along the first row: \[ = -\lambda \text{det} \begin{bmatrix} -1-\lambda & 6 \\ -1 & 4-\lambda \end{bmatrix} - 1 \text{det} \begin{bmatrix} 2 & 6 \\ 1 & 4-\lambda \end{bmatrix} + (-3) \text{det} \begin{bmatrix} 2 ___ _______ _________ ______ _____ ______ __________ _____ ___ __________ ___ _____.
________ ________ _______ ____ _________ _____ _________ ___ ___ _________ ____.
___ _________ __________ ________ _____ ___ ________.
_____ _________ __________ ____ ________ ____ _____ __________.
___ _______ ____ _________ __________ ________.
_________ ____ _____ ___ ________ ________ ___ _________ ___ ____ ______ __________.
___ __________ ___ _____ __________ ___ ______ __________ ___.
____ ______ ____ ________ _______ ______ ____ __________ ___ ____.
____ _________ _______ ______ ________ ______ ____ _____ _______.
_____ ______ ____ ______ ______ ____ ___.
____ _____ ________ ____ _______ ______.
____ __________ _________ ____ _______ ___ ______ ______ _________ ___.
__________ ______ _______ ______ ________ ______ _____ ___ _________ _____ __________ ________.
_____ _______ _____ ______ _____ __________ _________ ________ _____.
___ _____ ____ _______ __________ ____.
__________ _______ ________ ____ ____.
_______ _____ ___ ___ __________ ________ _____.
_______ _______ ________ ________ _________ ____ ____.
_____ _____ _____ _____ __________ _____ __________ _______ ______ ___ _________.
_______ _______ __________ __________ ________.
_____ ____ _________ __________ __________ __________.
___ __________ _____ ___ _______ __________ _________ ____ _______ _________ _____ ______.
________ _____ _____ __________ _______ _____.
____ _________ _____ ________ ___ _______ __________ ______ __________ ____ ____.
____ __________ ___ ______ _____ ___ ____ _____ _________.
_________ _________ ________ _____ _____ ___ _________ _________.
___ _____ ___ ___ _____ __________ _______ _________ ______ ______.
__________ _________ ____ ____ ____ ________.
_________ ___ ______ _______ _______ ________ __________.
____ _______ _________ _______ __________ ________.
________ __________ ________ _______ ______ __________ ________.
_________ _____ ______ ________ _________ _________ ________ ____ ____ _________ ______.
________ ____ ______ __________ _________ __________ ___ ________ ________ _____ ________.
____ _________ _________ _______ _____ __________ ________ ___ __________.
_________ ___ ____ _____ __________ _________.
________ _____ ___ __________ _____ _________ __________ ________.
__________ __________ __________ _______ ________ ______ ____ _____.
____ ______ ________ ______ _________ ______ ______ ________ ____ _______.
_______ ____ __________ _________ ___ _________ ____ ________ ___.
________ _____ ___ ___ ________ ______ __________ ____ ___ ______ __________.
_______ ______ _____ ______ _________ ___.
________ ____ ____ __________ _______ _________ ___.
_______ __________ ________ __________ _______ __________ ________ _______.
________ ____ __________ ______ _______ _________ ______ ______ _______ __________ _____ _________.
______ ___ __________ ____ _________ _________ ______ ___.
______ _________ _______ _________ __________ ______ _______.
____ ________ _______ __________ __________ __________ ________ _______.
_______ _____ _____ __________ ______ _________ ____ ___.
___ _________ ___ ___ ___ _________.
__________ _________ _____ ______ _________ ___ ________ _______ ________.
_____ ____ ________ _____ __________ _________ ______ ______ ______.
__________ _______ ______ _______ ______ ___ ____ ______ _______ _______.
___ __________ ____ _____ ______ _________ ____ ________ ____.
___ _________ ____ _____ _____ ____ ________ ____ ___ ____ _______ _______.
________ ___ ______ ____ _________ _______ ___.
__________ ____ _________ _______ ____ _______ ___ ____ _____.
______ __________ ____ ___ ______ ______ _________ _________ _____ __________.
_________ _______ __________ _____ ____ ________ _______ _______ ____ _____.
___ __________ ______ ___ ____ _____ ___ ________ ________ _________.
__________ ___ _____ ______ ___ ___ ____ _____ _____ ________ ___ _________.
____ __________ _________ ____ _____ ______ __________ ___ ____ ___ ______ _________.
_______ _______ _____ _______ ___.
_________ ____ ________ ______ ____ _________ ______ _____ ______ __________ ________.
___ ___ ________ _________ ___.
_________ _____ ____ _________ ___ ____ _____ ________ ___ ____ _________ ______.
__________ __________ ____ _______ ___.
___ ______ _________ _______ _________ ____ __________ ____ _______ _____ _____.
_________ _______ _________ __________ _______.
____ ____ ______ ___ _____ ___ _____ ____.
____ _____ ____ ____ _____ _________ __________ _____ ______.
___ ______ _________ ____ ______ ___ _________ _____ ___ ___.
________ _________ ________ ________ ______ _______ _______ _______.
________ __________ _______ __________ ______ ________ __________.
_______ ________ ___ _________ ____ ___ ______ ______.
______ _______ __________ _______ ___ ____.
____ ________ ____ ____ ___ ______ __________ ________ ___ _________.
_________ ___ ______ ______ _________.
___ _____ ___ _________ ____.
____ _________ _________ ____ ________ ___ _____ __________ _____.
_____ _______ ________ _______ _______ _______ _________ _________ ___ __________ ____ _________.
_________ ______ _____ _______ __________ ______ _________ __________ __________ _________ ___ _______.
__________ _____ __________ __________ ______ _____ __________ __________ __________ _________.
______ ________ _____ _____ ______ _______ ____ __________ ____ _____.
___ _________ _________ _______ ___ _________.
____ ________ _____ _____ __________ _______ __________ _________ _____ _________.
__________ ______ _______ _________ ____ _______ _____ _________ _________.
__________ __________ ___ ____ ______ ________ _______ ________ ____ ___ _________ ____.
_________ _________ ____ ____ _____ __________ ___ _______ ________.
________ __________ ____ _______ ________ ______ _______ __________.
__________ _________.
Get Full Answer on WhatsApp