# Write the given matrix equation as a system of linear equations without matrices.[(2,0,-1),(0,3,0),(1,1,0)][(x),(y),(z)]=[(6),(9),(5)]

Write the given matrix equation as a system of linear equations without matrices.
$\left[\begin{array}{ccc}2& 0& -1\\ 0& 3& 0\\ 1& 1& 0\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{c}6\\ 9\\ 5\end{array}\right]$

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Here, $\left[\begin{array}{ccc}2& 0& -1\\ 0& 3& 0\\ 1& 1& 0\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{c}6\\ 9\\ 5\end{array}\right]$
the dimension of
$\left[\begin{array}{ccc}2& 0& -1\\ 0& 3& 0\\ 1& 1& 0\end{array}\right]$ is $3\cdot 3$
\$ dimension of $\left[\begin{array}{c}x\\ y\\ z\end{array}\right]$ is $3\cdot 1$
so, the column of $\left[\begin{array}{ccc}2& 0& -1\\ 0& 3& 0\\ 1& 1& 0\end{array}\right]$ matrix is equal to row $\left[\begin{array}{c}x\\ y\\ z\end{array}\right]$
Thus multiplication is possible
by the definition of matrix equality, we have system of linear equations
$⇒2x-z=0$
$3y=0$
$x+z=0$