Hello,
Can you please help me solve this probelm:
Solve the system of equations. Please show all work. ALSO PLEASE USE GAUSSIAN ELIMINATION METHOD TO SOLVE!!!
x+y+z=0, 2x+5y+2z=-9, -x+8y-3z=-25
.
system Ax=b is
augmented matrix is
1 | 1 | 1 | 0 |
2 | 5 | 2 | -9 |
-1 | 8 | -3 | -25 |
by gauss elimination method convert into row echelon form
Add (-2 * row1) to row2
1 | 1 | 1 | 0 |
0 | 3 | 0 | -9 |
-1 | 8 | -3 | -25 |
Add (1 * row1) to row3
1 | 1 | 1 | 0 |
0 | 3 | 0 | -9 |
0 | 9 | -2 | -25 |
Divide row2 by 3
1 | 1 | 1 | 0 |
0 | 1 | 0 | -3 |
0 | 9 | -2 | -25 |
Add (-9 * row2) to row3
1 | 1 | 1 | 0 |
0 | 1 | 0 | -3 |
0 | 0 | -2 | 2 |
Divide row3 by -2
1 | 1 | 1 | 0 |
0 | 1 | 0 | -3 |
0 | 0 | 1 | -1 |
reduced system is
.
from last row
.
from second row
.
from first row
.
.
solution is
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