+0

x + y − z = −5

0
144
1

x + y − z = −5

x + 2y + 3z = −12

2x − y − 13z = 13

Guest May 12, 2017
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#1
+18629
+1

x + y − z = −5

x + 2y + 3z = −12

2x − y − 13z = 13

$$\text{Let Matrix } A = \begin{pmatrix} 1 & 1 & -1 \\ 1 & 2 & 3 \\ 2 & -1 & -13 \end{pmatrix}$$

$$\text{Let } \vec{r} = \begin{pmatrix} -5 \\ -12 \\ 13 \end{pmatrix}$$

$$\text{Let } \vec{x} = \begin{pmatrix} x \\ y \\ z \end{pmatrix}$$

$$\text{Let Matrix } A^{-1} = \begin{pmatrix} -23 & 14 & 5 \\ 19 & -11 & -4 \\ -5 & 3 & 1 \end{pmatrix}$$

Then

$$\begin{array}{|rcll|} \hline A\vec{x} &=& \vec{r} \\ \vec{x} &=& A^{-1}\vec{r} \\ \vec{x} &=& \begin{pmatrix} -23 & 14 & 5 \\ 19 & -11 & -4 \\ -5 & 3 & 1 \end{pmatrix}\cdot \begin{pmatrix} -5 \\ -12 \\ 13 \end{pmatrix} \\ \vec{x} &=& \begin{pmatrix} 12 \\ -15 \\ 2 \end{pmatrix} \\ \hline \end{array}$$

x =  12

y = -15

z =  2

heureka  May 12, 2017

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