Answer
$AX=B$
$\left[\begin{array}{lll}
1 & -1 & 1\\
4 & 2 & 1\\
4 & -2 & 1
\end{array}\right]\left[\begin{array}{l}
x\\
y\\
z
\end{array}\right]=\left[\begin{array}{l}
-6\\
9\\
-3
\end{array}\right]$
X=$\left[\begin{array}{l}
2\\
3\\
-5
\end{array}\right]$
Work Step by Step
In matrix form, the linear system is written as
$AX=B$
$\left[\begin{array}{lll}
1 & -1 & 1\\
4 & 2 & 1\\
4 & -2 & 1
\end{array}\right]\left[\begin{array}{l}
x\\
y\\
z
\end{array}\right]=\left[\begin{array}{l}
-6\\
9\\
-3
\end{array}\right]$
Technology used: the free online calculator at
www.geogebra.org/classic/cas
The syntax for defining a matrix:
A:= { { row 1}, {row 2} ... { row n} },
(the elements in rows are delimited with commas)
(A "colon equals" assigns the matrix to A).
The command for $A^{-1}$ is Invert ( A ).
The solution X=s
s:=Invert ( A )$\cdot b$
(s "colon equals" assigns the matrix to s).
The solution (s=X)
X=$\left[\begin{array}{l}
2\\
3\\
-5
\end{array}\right]$
Finally we check if AX=B. It is.
Screenshot:
