SOLUTION: 2x-y+3z=0 x+2y-z=5 2y+z=1 use gaussian reduction method matrix to solve the following linear system

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Question 1090280: 2x-y+3z=0
x+2y-z=5
2y+z=1
use gaussian reduction method matrix to solve the following linear system
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
2x-y%2B3z=0
x%2B2y-z=5
+2y%2Bz=1
Rewrite the system in matrix form:
matrix%283%2C4%2C2%2C-1%2C3%2C0%2C1%2C2%2C-1%2C5%2C0%2C2%2C1%2C1%29

divide the 1 row by 2:

matrix%283%2C4%2C1%2C-1%2F2%2C3%2F2%2C0%2C1%2C2%2C-1%2C5%2C0%2C2%2C1%2C1%29


Add (-1 * row1) to row2
matrix%283%2C4%2C1%2C+-1%2F2%2C+3%2F2%2C+0%2C0%2C5%2F2%2C-5%2F2%2C5%2C0%2C2%2C1%2C1%29


Divide row2 by 5%2F2
matrix%283%2C4%2C1%2C+-1%2F2%2C+3%2F2%2C+0%2C0%2C1%2C-1%2C2%2C0%2C2%2C1%2C1+%29


Add (-2 * row2) to row3:
matrix%283%2C4%2C1%2C+-1%2F2%2C+3%2F2%2C+0%2C0%2C1%2C-1%2C2%2C0%2C0%2C3%2C-3%29


Divide row3 by 3:
matrix%283%2C4%2C1%2C+-1%2F2%2C+3%2F2%2C+0%2C0%2C1%2C-1%2C2%2C0%2C0%2C1%2C-1%29


Add (1 * row3) to row2:



Add (-3%2F2+* row3) to row1:



Add (1%2F2 * row2) to row1:



Answer:
x+=+2
y=+1
z=+-1