Use matrices to solve the system of eqs (if possible). Use Gauss-Jordan elimination. (If no solution, enter NO SOLUTION. If system is dependent, set z = a and solve for x and y in terms of a.)

Question

2x+2y-z= 14

x-3y+z= -30

-x+y =12

(x,y,z) = ______

Answer 1

2 2 -1 14

1 -3 1 -30

-1 1 0 12

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Row3 = Row2 + Row3;

row1 = -2 * row2 + row1;

0 8 -3 74

1 -3 1 -30

0 -2 1 -18

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row1 = 4 * row3 + row1

0 0 1 2

1 -3 1 -30

0 -2 1 -18

per equation #1 : z = 2

per equation #3: -2y +z = -18

-2y + 2 = -18

-2y = -20

y = 10

Per equation #2:

x - 3(10) + 2 = -30

x - 30 + 2 = -30

x - 28 = -30

x=-2

x=-2, y=10, z = 2