Solve this system using an inverse matrix.

x=

y=

z=

Write the system in the matrix form AX=B

Adjoin matrix A with the identity matrix and use
Gauss-Jordan elimination to find the inverse of A (A^{-1}):

E_{3}=E_{3}-E_{2}

Switch E_{2 }withE_{3}

E_{3}=E_{3}-E_{2}

E_{3}=E_{3}/2

E_{1}=E_{1}-E_{3}

Multiply B by A^{-1} on the left to obtain the
solution:

X=A^{-1}B

The solution of the system is x=2, y=6, and z=-1