solve the following system of equations by using matrix method:

$x+y=1$

$7x+7y=7$.

Using matrix method, solve the following system of equations:

$x-2y+3z=6$

$x+4y+z=12$

$x-3y+4z=1$.

Using matrix method, solve the following system of equations:

$x+y+z=6$

$x-y+z=2$

$2x+y-z=1$.

Using matrix method, solve the following system of equations:

$x+y+z=9$

$2x+5y+7z=52$

$2x+y-z=0$.

Using matrix method, solve the following system of equations:

$x+2y=5$

$y+2z=8$

$2x+z=5$.

Using matrix method, solve the following system of equations:

$3x+y+z=1$

$2x+2z=0$

$5x+y+2z=2$.

Using matrix method, solve the following system of equations:

$2x-y+z=3$

$-x+2y-z=-4$

$x-y+2z=1$.

State the condition under which the following equations have a unique solution:

$x+2y-2z+5=0$

$-x+3y+4=0$

$-2y+z-4=0$.

Using Martin's rule, find the unique solution of the above system of linear equations.