Use matrices to solve the system of linear equations

Question

Use matrices to solve the system of linear equations, if possible. Use Gauss-Jordan elimination. (If not possible, enter IMPOSSIBLE. If the system is dependent, express x and y in terms of the parameter a.)

 
2x− y + 3z= 21
2y− z= 14
7x− 5y= 18

Answer 1

Hello Ashlyn Please follow line by line.

2x -y +3z =21.
2y -z =14.
7x -5y =18.
_________________________.

2 -1 3 21.
(3) 0 2 -1 14 3x r2 +r1 --> r1.
7 -5 0 18.


2 5 0 63 r1 + r3 ----> r1.
0 2 -1 14.
7 -5 0 18.


9 0 0 81 9x =81.
0 2 -1 14 ___ ____.
7 -5 0 18 9 9 x= 9.


7x -5y =18.

7(9) -5y =18.

63 -5y =18.

-63 -63.
____________________.
-5y = -45.
____ ____.
-5 -5.

y = 9.


2y -z =14.

2(9) -z =14.

18 -z =14.
-18 -18.
____________________.
-z = -4
(-1) -z = -4 (multiply by -1 ).

z= 4.
Solution Set = (x=9 y=9 z=4).

Hope this helps.