## Algebra and Trigonometry 10th Edition

$\begin{bmatrix} 1 & -4 & 3 & -2 & |9\\ 3 & -2 & 1 & -4 & |-13\\ -4 & 3 & -2 & 1 & |-4\\ -2 & 1 & -4 & 3 & |-10\\ \end{bmatrix}$ ~ $\begin{bmatrix} 1 & -4 & 3 & -2 & |9\\ 0 & 10 & -8 & 2 & |-40\\ 0 & -13 & 10 & -7 & |32\\ 0 & -7 & 2 & -1 & |8\\ \end{bmatrix}$ ~ $\begin{bmatrix} 1 & -4 & 3 & -2 & |9\\ 0 & 5 & -4 & 1 & |-20\\ 0 & -13 & 10 & -7 & |32\\ 0 & -7 & 2 & -1 & |8\\ \end{bmatrix}$ ~ $\begin{bmatrix} 1 & -4 & 3 & -2 & |9\\ 0 & 5 & -4 & 1 & |-20\\ 0 & 0 & 1 & 11 & |50\\ 0 & 0 & -18 & 2 & |-100\\ \end{bmatrix}$ ~ $\begin{bmatrix} 1 & -4 & 3 & -2 & |9\\ 0 & 5 & -4 & 1 & |-20\\ 0 & 0 & 1 & 11 & |50\\ 0 & 0 & -9 & 1 & |-50\\ \end{bmatrix}$ ~ $\begin{bmatrix} 1 & -4 & 3 & -2 & |9\\ 0 & 5 & -4 & 1 & |-20\\ 0 & 0 & 1 & 11 & |50\\ 0 & 0 & 0 & 100 & |400\\ \end{bmatrix}$ Back-Substitution: W: 100w = 400 w = 4 Z: z + 4(11) = 50 z + 44 = 50 z = 6 Y: 5y - 4(6) + 4 = -20 5y - 24 + 4 = -20 5y - 20 = -20 5y = 0 y = 0 X: x - 4(0) + 3(6) - 2(4) = 9 x + 18 - 8 = 9 x + 10 = 9 x = -1 In Total: x = -1 y = 0 z = 6 w = 4