SOLUTION: Solve the system of equations by finding a row echelon form for the augmented matrix. x - 3y + 3z = 19 2x -y

SOLUTION: Solve the system of equations by finding a row echelon form for the augmented matrix. x - 3y + 3z = 19 2x -y - 9z= -32 -5x+10y+z=-21

Question 1134169: Solve the system of equations by finding a row echelon form for the augmented matrix.
x - 3y + 3z = 19
2x -y - 9z= -32
-5x+10y+z=-21

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
The augmented matrix is
:
1 -3 3 19
2 -1 -9 -32
-5 10 1 -21
:
We perform a series of row operations to achieve row echelon form, let Rn be the nth row of the matrix
:
R3 +5R1
:
5 -15 15 95
2 -1 -9 -32
0 -5 16 74
:
R1/5
:
1 -3 3 19
2 -1 -9 -32
0 -5 16 74
:
R2 -2R1
:
2 -6 6 38
0 5 -15 -70
0 -5 16 74
:
R2 +R3
:
2 -6 6 19
0 5 -15 -70
0 0 1 4
:
R1/2, R2/5
:
1 -3 3 19
0 1 -3 -14
0 0 1 4
:
The above matrix is our row echelon matrix, then
:
x -3y +3z = 19
y -3z = -14
z = 4
:
y -3(4) = -14
y = -2
:
x -3(-2) +3(4) = 19
x = 1
:
**************************************************
x = 1, y = -2, z = 4
:
check the answers
:
x - 3y + 3z = 19
:
1 -3(-2) +3(4) = 19
19 = 19
:
2x -y - 9z = -32
:
2(1) -(-2) -9(4) = -32
-32 = -32
:
-5x +10y +z = -21
:
-5(1) +10(-2) +4 = -21
-21 = -21
:
answer checks
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