Matrices Question

[jrr6415sun]

Can someone please tell me how can I go about transforming a linear equation?

for example lets say I have

X = 1B + C
Y = C - B - A
Z = A + C

I want to turn the equation into something like

A = (X,Y,Z)
B = (X,Y,Z)
C = (X,Y,Z)

I figure I need to use matricies,can someone help me

 

[pka]

Is this what you want?
\(\displaystyle \L
\left[ {\begin{array}{c}
{\rm{X}} \\
{\rm{Y}} \\
{\rm{Z}} \\
\end{array}} \right] = \left[ {\begin{array}{rrr}
0 & 1 & 1 \\
{ - 1} & { - 1} & 1 \\
1 & 0 & 1 \\
\end{array}} \right]\left[ {\begin{array}{c}
{\rm{A}} \\
{\rm{B}} \\
{\rm{C}} \\
\end{array}} \right]\)

 

[jrr6415sun]

no i need it to get the answer so like

A = X + Y + Z
B = X + Y + Z
C = X + Y + Z

 

[pka]

\(\displaystyle \L
\begin{array}{l}
\left[ {\begin{array}{rrr}
0 & 1 & 1 \\
{ - 1} & { - 1} & 1 \\
1 & 0 & 1 \\
\end{array}} \right]^{ - 1} = \frac{1}{3}\left[ {\begin{array}{rrr}
{ - 1} & { - 1} & 2 \\
2 & { - 1} & { - 1} \\
1 & 1 & 1 \\
\end{array}} \right] \\
\left[ {\begin{array}{c}
{\rm{A}} \\
{\rm{B}} \\
{\rm{C}} \\
\end{array}} \right] = \frac{1}{3}\left[ {\begin{array}{rrr}
{ - 1} & { - 1} & 2 \\
2 & { - 1} & { - 1} \\
1 & 1 & 1 \\
\end{array}} \right]\left[ {\begin{array}{c}
{\rm{X}} \\
{\rm{Y}} \\
{\rm{Z}} \\
\end{array}} \right] \\
\end{array}\)

 

[jrr6415sun]

why thank you

that makes sense