Word Count : 728

---

We are asked to solve the given system of simultaneous equations using Cramer’s Rule manually. The equations are: 1. $x + 2y + z = 3$ 2. $2x - y + 2z = 1$ 3. $3x + y + z = 0$ *(I assume the third equation is $3x + y + z = 0$, since the image is incomplete)* --- ### Step 1: Write in matrix form $$ \begin{aligned} \begin{bmatrix} 1 & 2 & 1 \\ 2 & -1 & 2 \\ 3 & 1 & 1 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 3 \\ 1 \\ 0 \end{bmatrix} $$ Let $A$ be the coefficient matrix and $\Delta = \det(A)$. $$ A = \begin{bmatrix} 1 & 2 & 1 \\ 2 & -1 & 2 \\ 3 & 1 & 1 \end{bmatrix} $$ --- ### Step 2: Compute $\Delta = \det(A)$ Use cofactor expansion along the first row: $$ \Delta = 1 \begin{vmatrix} -1 & 2 \\ 1 & 1 \end{vmatrix} - 2 \begin{vmatrix} 2 & 2 \\ 3 & 1 \end{vmatrix} + 1 \begin{vmatrix} 2 & ___ _______ _____ ___ _________ ____.
___ _______ _______ ___ __________.
_____ _______ __________ ___ _______ ___.
_______ ______ _______ _________ ____ ______ ___ __________ _______.
_____ ____ _____ ___ _____ __________ _______.
___ _________ ________ _________ ________ _____ ______ ____.
___ _____ ____ _______ ___ _______ __________ ____ _____ _______ __________.
______ ____ _______ __________ ________ _____ ___ _________ _______ ____.
_________ _____ ________ ________ _____ _______ ________.
__________ ____ ________ _____ _______ ________ _____ ________ _________ _______.
_________ __________ ____ ____ ___ ________ ________ ___ _________ _____ ___ __________.
__________ _____ ________ __________ _________ ________.
__________ ____ ______ __________ _______ __________ ______ __________.
_______ __________ _____ ________ _______ ___.
_____ _______ ________ _____ _________ ________ ________ _______ _____ _____.
__________ __________ ___ _____ _________ _________ __________ _________.
___ ________ ____ __________ _________ ____ ___ ___ _________ __________ _____.
________ ____ ___ _____ ______ ___ ______ __________.
__________ ________ ________ ________ _________ _________ ____ _____.
________ ______ __________ _____ ____ _________ __________ _________ __________ ___ ____ ________.
_______ ______ _____ ____ ________.
_____ _______ _______ _____ ___ ______ _________ ___ __________ __________ _________.
_______ ______ ___ _______ ___ __________ ______ ________ _____ ___ _______ _____.
________ _______ ________ _________ ____ _______ _____ ________ ____ _________ ____ __________.
_____ _____ _________ ______ ______ _______ ______ ________ ______.
__________ _______ __________ _______ ________ __________ ___ _________ ______.
________ _________ ____ __________ ________ _______ ______ ___ ________ ____ __________ _____.
_____ _________ _____ ________ ____ _________ ___ _________.
___ ____ _____ ____ _____ _____ _______ __________.
____ ___ _____ ___ _______ ________ _____ ___ __________ _________ ______.
__________ ______ __________ __________ _______ _____ __________ ______.
________ _______ ___ _________ _____ ____ _________ ________ _____ _________ ____.
________ _____ _______ _______ _________ ___.
_____ ______ ______ ________ ___ ______ _____ ____ __________ ______.
___ __________ ___ ___ _________ ____ ____ _______ _______ ________.
______ __________ ______ __________ _____ ___ __________ ________ _____ __________ ___.
___ ___ ______ ________ ______ __________ _______ _______ _______.
_____ _________ __________ _____ _______ ____ ________ ___ __________ _____ ____ _____.
___ _______ _____ _________ __________ ___ ___ _____.
_________ _____ __________ ______ ___.
____ ___ ___ _______ _________ __________.
_______ ______ _______ _________ _____ __________ ________ _________ ________.
__________ _______ ________ ______ __________.
_____ ___ _________ ________ ________ _______ _________ ________ ____ ___.
__________ ______ _________ ______ _______ ______ ______.
__________ _________ __________ ____ ____ _____ _________ _______ __________.
____ ______ ____ ___ _______.
_______ _________ ____ _______ ________ _____ __________ ______.
__________ _________ ________ _____ ________ _______ ______ __________ __________ _______ ______.
________ __________ _____ _________ __________.
______ ___ ______ _____ ____ ______.
_____ ____ ______ _____ ________ ______ __________ ___ _________.
_________ _____ ________ _______ __________ ______ ____ ____ __________ _____ ____ _____.
_______ _____ __________ ______ ________.
_______ ________ ____ _______ __________ ________ ________.
_______ _____ _________ _____ ___ _________ __________ ___ ______ _____ _____.
____ ________ _________ _____ __________ _______ _____.
____ __________ _____ ______ ___ ______ ______.
____ _________ __________ ___ _____ _______.
___ __________ _______ ________ _____ ___.
____ _____ _______ ________ ___ ____ ________ ______ ________ ___ _________.
__________ ______ ______ _____ ___ _____ ___ __________ _________ _______ ______ ___.
__________ ________ _____ _________ ___ _________ _____ __________ _________ ____.
______ __________ ______ __________ _______ _______ ____.
Get Full Answer on WhatsApp