## Math Problem Statement

write the matrix set up ${\displaylines\sum3x+2y-z=9\\ x-y+3z=3_{}\\ 2x+3y-4z=6}$

## Solution

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## Math Problem Analysis

### Mathematical Concepts

Linear Algebra

Matrix Equations

Systems of Linear Equations

### Formulas

Matrix form: AX = B

Coefficient matrix: A = \begin{pmatrix} 3 & 2 & -1 \\ 1 & -1 & 3 \\ 2 & 3 & -4 \end{pmatrix}

Variable matrix: X = \begin{pmatrix} x \\ y \\ z \end{pmatrix}

Constant matrix: B = \begin{pmatrix} 9 \\ 3 \\ 6 \end{pmatrix}

### Theorems

Gaussian Elimination

Matrix Inversion

Cramer's Rule

### Suitable Grade Level

Grades 10-12