SOLUTION: x-z=-3 y+z=9 x+z=7 solve the following linear system by using gaussian reduction method matrix

Question 1090279: x-z=-3
y+z=9
x+z=7
solve the following linear system by using gaussian reduction method matrix
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The matrix for the given equations is

We first want to get "1 0 0" in column 1. It is already nearly the way we want it; we just need to get a 0 in row 3. To do that, we can replace row 3 with (row 3 - row 1).
R3 <-- R3-R1: 1-1=0; 0-0=0; 1-(-1)=2; 7-(-3)=10:

Next we can make smaller numbers in the matrix by dividing row 3 by 2:

After this, the second column is already the way we want it. So now we use row 3 to get "0 0 1" in column 3.
R1 <-- R1+R3: 1+0=1; 0+0=0; 1+(-1)=0; -3+5=2
R2 <-- R2-R3: 0-0=0; 1-0=1; 1-1=0; 9-5=4

The solution to the system of equations is x=2, y=4, z=5.

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