Word Count : 654

---

To find the minimal polynomial of the given matrix \[ A = \begin{bmatrix}2 & 1 & 0 & 1 \\ -1 & 0 & 0 & 1 \\ -2 & -2 & -1 & 3 \\ 0 & 0 & 0 & 1\end{bmatrix} \] we proceed with the following steps: ### Step 1: Compute the Characteristic Polynomial The characteristic polynomial is given by: \[ \chi_A(\lambda) = \det(A - \lambda I) \] \[ A - \lambda I = \begin{bmatrix} 2 - \lambda & 1 & 0 & 1 \\ -1 & -\lambda & 0 & 1 \\ -2 & -2 & -1 - \lambda & 3 \\ 0 & 0 & 0 & 1 - \lambda \end{bmatrix} \] Expanding along the fourth column (which has a single nonzero element): \[ \det(A ______ __________ __________ ____ _________ _____ ______.
_________ ______ ___ _______ _________ ____.
_______ _________ _________ __________ ________ _______ _____.
___ _____ _____ __________ ________ ____.
______ ______ _____ _______ __________ _________.
______ ____ ____ ______ ____ __________ _____ ______ ______.
___ _________ ______ _______ ___ _____ ____ ______ ____ _________ _______ ___.
_________ __________ _______ ________ __________ _____ _________ ______ ___ ______ _____ ____.
__________ _______ __________ _________ ____ _____ ______ _____.
___ __________ ____ __________ _________ _________ _______.
___ ________ __________ __________ ___ ______ __________ _____ __________.
_____ __________ _____ __________ ______ __________.
___ ___ ____ __________ _______ _________.
______ _____ ________ _________ ____ ________ ___ _________ _______ __________ ____ ________.
________ ___ _________ _____ ___ ___.
___ ______ _________ _______ _____ _____ ________ ______.
________ ______ ____ _______ _____ _________ _______ ____ _________ _______ ________.
____ __________ ______ ________ _________ _______.
_________ _______ ________ ___ __________.
___ _____ __________ _______ _____ ______ ________ _______ ____ _____.
__________ ____ _______ _____ ________ _______ ________ ________ _________ ____ ___.
__________ ___ ___ ________ _________ ___ _____ _________ __________ ____.
____ _________ ___ ______ __________ __________ _____.
___ _______ ______ _______ _______ ___ __________.
______ _________ ________ _______ _____.
_________ __________ __________ ____ ______ ______.
_________ __________ __________ ____ ____.
________ _______ ________ _____ ___.
__________ __________ ________ ______ ________ ________ ________ _____ ______ ____.
___ __________ _________ _________ ______.
______ _____ _________ ______ ____.
____ ________ _________ _________ _________ ____ _______ ____ _________ ________ ____ ____.
_______ _________ ______ ______ _____ ________.
____ ________ _______ ____ ______.
_______ __________ ____ __________ _____ ______.
_________ _________ _________ __________ __________ _____ ________ ____ _______ ________ ______.
_________ __________ _____ ___ ______ ______ ______.
_________ _______ ___ ___ ___ _________ _____ _________ _______ ________.
___ __________ __________ _______ ___ ____ __________ ___ __________.
_____ ___ _____ _______ __________ ________ _______ _____.
_______ ___ _________ ______ ____ __________ ________.
____ ______ _____ _____ _____ ________ ________ _____.
_____ ____ _______ _________ ______ ______ __________ ___ ________ _____ ______ ______.
______ ___ __________ _____ ________ _______ __________ __________ _______ _______ ___ ______.
__________ ______ __________ __________ ____ ___ __________ _____ _______ ________ _____ ______.
______ _________ ______ ______ _________ _______ _______ ____ _________ ___ ________.
________ __________ ____ _____ _________ _______ ____ __________ _____ __________ ____.
________ ______ ______ ____ ________.
_________ _____ ______ _____ _____ ____ ___ __________ _________.
_________ _______ ______ _____ _____ ______ _______ ________.
_____ _____ ____ __________ _______ _______ ________ _________ __________ ____ _______.
_______ _______ _____ ________ ________ __________ ____ ______ _______ __________ ___.
_____ ______ __________ _______ ________ _______ _______ __________ ________ _________.
________ _______ ________ ______ ____ ____ ___ ________ __________ ____.
____ _________ ___ ________ ______.
_________ _______ ___ __________ ____ __________ __________ ________ ______ _______ __________ _____.
__________ ____ ____ ________ _________ ________ _____ ___.
____ ___ ________ ___ ________ _________.
_________ ____ ___ ________ __________ ________ ____.
_________ ___ ___ __________ ____ ______ __________ ____ ___ _________.
______ ___ __________ ____ ____ ______ __________ __________ ____.
_________ __________ ____ _____ ___ ___ _______ ___.
_____ __________ _______ ____ ____ ______ ______ _____ _______ _____.
____ _____ ____.
Get Full Answer on WhatsApp