# Write the values of $$x-y+z$$ from the following equation : $\begin{bmatrix} x+y+z \\ x+z \\ y+z \end{bmatrix} = \begin{bmatrix} 9 \\ 5 \\ 7 \end{bmatrix}$

Toolbox:
• If the order of 2 matrices are equal, their corresponding elements are equal, i.e, if $A_{ij}=B_{ij}$, then any element $a_{ij}$ in matrix A is equal to corresponding element $b_{ij}$ in matrix B.
Given :
$\begin{bmatrix}x+y+z\\x+z\\y+z\end{bmatrix}=\begin{bmatrix}9\\5\\7\end{bmatrix}$
$x+y+z=9$
$x+z=5$
$y+z=7$
Let us solve these equations to solve for $x,y$ and $z$
$y+5=9$
$y=4$
$4+z=7$
$z=3$
$\therefore x+4+3=9$
$x=2$