SOLUTION: Solve the system of equations using the methods of matrix row reduction. 2x+y+2z=0 4x+3y-z=1 5x-4y+3z=-41 What is the solution? Thank you.

Algebra ->  Matrices-and-determiminant -> SOLUTION: Solve the system of equations using the methods of matrix row reduction. 2x+y+2z=0 4x+3y-z=1 5x-4y+3z=-41 What is the solution? Thank you.      Log On


   

Question 985488: Solve the system of equations using the methods of matrix row reduction.
2x+y+2z=0
4x+3y-z=1
5x-4y+3z=-41
What is the solution?
Thank you.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

2x%2By%2B2z=0
4x%2B3y-z=1
5x-4y%2B3z=-41
------------------------------


Step 1: Swap row 3 and 1




Step 2: Divide row 1 by 5




Step 3: Subtract (4+%2A+row+%7B%7B%7B1) from row 2



Step 4: Subtract (2 * row 1) from row 3




Step 5: Divide row 2 by 6.2




Step 6:
Subtract (2.6+* row+2) from row 3



Step 7: Divide row 3 by 2.226



Matrix is now in row echelon form
Step 8: Subtract (0.6 * row 3) from row 1




Step 9: Subtract (-0.548 * row 3) from row 2



Step 10: Subtract (-0.8 * row 2) from row 1


%28matrix%283%2C4%2C%0D%0A1%2C0%2C0%2C-4%2C%0D%0A0%2C1%2C0%2C6%2C%0D%0A0%2C0%2C1%2C1%29+%29
Matrix is now in reduced+row echelon form.
solution:
x=-4
y=6
z=1
check:
2x%2By%2B2z=0
2%28-4%29%2B6%2B2%2A1=0
-8%2B8=0
0=0