SOLUTION: Solve the system using an augmented matrix in the reduced row echelon form. Be sure to show all elementary row operations. x+y+z=-1 x-y+5z=1 2x+y+z=-4 I submitted this ea

Algebra ->  Matrices-and-determiminant -> SOLUTION: Solve the system using an augmented matrix in the reduced row echelon form. Be sure to show all elementary row operations. x+y+z=-1 x-y+5z=1 2x+y+z=-4 I submitted this ea      Log On


   

Question 1134302: Solve the system using an augmented matrix in the reduced row echelon form. Be sure to
show all elementary row operations.
x+y+z=-1
x-y+5z=1
2x+y+z=-4
I submitted this earlier but accidentally put z instead of the 2
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

x%2By%2Bz=-1
x-y%2B5z=1
2x%2By%2Bz=-4

matrix%283%2C4%2C1%2C1%2C1%2C-1%2C1%2C-1%2C5%2C1%2C2%2C1%2C1%2C-4%29
Make zeros in column 1 except the entry at row 1, column 1 (pivot entry).
Subtract row 1 from row+2:
matrix%283%2C4%2C%0D%0A1%2C1%2C1%2C-1%2C%0D%0A0%2C-2%2C4%2C2%2C%0D%0A2%2C1%2C1%2C-4%29
Subtract row 1 multiplied by 2 from row 3
matrix%283%2C4%2C%0D%0A1%2C1%2C1%2C-1%2C%0D%0A0%2C-2%2C4%2C2%2C%0D%0A0%2C-1%2C-1%2C-2%29
Make zeros in column 2 except the entry at row+2, column 2+(pivot entry).
Divide row 2 by -2:
matrix%283%2C4%2C%0D%0A1%2C1%2C1%2C-1%2C%0D%0A0%2C1%2C-2%2C-1%2C%0D%0A0%2C-1%2C-1%2C-2%29

Subtract row 2 from row 1:
matrix%283%2C4%2C%0D%0A1%2C0%2C3%2C0%2C%0D%0A0%2C1%2C-2%2C-1%2C%0D%0A0%2C-1%2C-1%2C-2%29
Add row 2 to row 3:
matrix%283%2C4%2C%0D%0A1%2C0%2C3%2C0%2C%0D%0A0%2C1%2C-2%2C-1%2C%0D%0A0%2C0%2C-3%2C-3%29
Make zeros in column 3 except the entry at row+3, column+3(pivot entry).
Add row 3 to row 1:

matrix%283%2C4%2C%0D%0A1%2C0%2C0%2C-3%2C%0D%0A0%2C1%2C-2%2C-1%2C%0D%0A0%2C0%2C-3%2C-3%29
Divide row 3 by -3:

matrix%283%2C4%2C%0D%0A1%2C0%2C0%2C-3%2C%0D%0A0%2C1%2C-2%2C-1%2C%0D%0A0%2C0%2C1%2C1%29
Add row 3 multiplied by 2 to row 2
matrix%283%2C4%2C%0D%0A1%2C0%2C0%2C-3%2C%0D%0A0%2C1%2C0%2C1%2C%0D%0A0%2C0%2C1%2C1%29
Answer: the reduced row echelon form is
A[ref]=matrix%283%2C4%2C%0D%0A1%2C0%2C0%2C-3%2C%0D%0A0%2C1%2C0%2C1%2C%0D%0A0%2C0%2C1%2C1%29