# Chapter 10 - 10.1 - Matrices and Systems of Equations - 10.1 Exercises - Page 711: 75

x = 4 y = -3 z = 2

#### Work Step by Step

NOTE: Gauss-Jordan elimination will reduce until the matrix is in reduced row-echelon form. $\begin{bmatrix} 1 & 0 & -3 & |-2\\ 3 & 1 & -2 & |5\\ 2 & 2 & 1 & |4\\ \end{bmatrix}$ ~ $\begin{bmatrix} 1 & 0 & -3 & |-2\\ 0 & 1 & 7 & |11\\ 0 & 2 & 7 & |8\\ \end{bmatrix}$ ~ $\begin{bmatrix} 1 & 0 & -3 & |-2\\ 0 & 1 & 7 & |11\\ 0 & 0 & -7 & |-14\\ \end{bmatrix}$ ~ $\begin{bmatrix} 1 & 0 & -3 & |-2\\ 0 & 1 & 7 & |11\\ 0 & 0 & 1 & |2\\ \end{bmatrix}$ ~ $\begin{bmatrix} 1 & 0 & 0 & |4\\ 0 & 1 & 0 & |-3\\ 0 & 0 & 1 & |2\\ \end{bmatrix}$ From reduced row-echelon form the solution is simple: x = 4 y = -3 z = 2

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