Question

Solve the following systems of linear equations using the Gaussian elimination method.
x + 2y − 3z = 1
2x + 5y − 8z = 4
3x + 8y − 13z = 7.

Answer 1

x1 + 2x2 - 3x3 = 1
2x1 + 5x2 - 8x3 = 4
3x1 + 8x2 - 13x3 = 7

Rewrite the system in matrix form and solve it by Gaussian Elimination (Gauss-Jordan elimination)
1 2 -3 1
2 5 -8 4
3 8 -13 7

R2 - 2 R1 → R2 (multiply 1 row by 2 and subtract it from 2 row); R3 - 3 R1 → R3 (multiply 1 row by 3 and subtract it from 3 row)
1 2 -3 1
0 1 -2 2
0 2 -4 4

R1 - 2 R2 → R1 (multiply 2 row by 2 and subtract it from 1 row); R3 - 2 R2 → R3 (multiply 2 row by 2 and subtract it from 3 row)
1 0 1 -3
0 1 -2 2
0 0 0 0

Answer:

The system of equations has a solution set:
x1 + x3 = -3
x2 - 2x3 = 2

Answer 2

no