+0  
 
0
307
1
avatar

x + y − z = −5

x + 2y + 3z = −12

2x − y − 13z = 13

Guest May 12, 2017
 #1
avatar+19632 
+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

 

laugh

heureka  May 12, 2017

12 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.