Final answer:
The system of equations is transformed to a triangular matrix using row operations to simplify to row echelon form for easier solution finding.
Step-by-step explanation:
To solve the system of equations 3x - 2y + z = 0, 6x + 2x +3z = -2, and 3x - 4y + 5z = 5 using row echelon form, we will perform row operations to simplify the system to a triangular matrix, where all elements below the main diagonal are zeros. Here are the steps:
- Write the system in matrix form.
[3 -2 1 | 0]
[8 0 3 | -2]
[3 -4 5 | 5]
- Use row operations to get zeros below the main diagonal.
[3 -2 1 | 0] R1
[0 16 1 | -2] R2 - 8/3 * R1
[0 -2 4 | 5] R3 - R1
- Continue with row operations until the matrix is in row echelon form.
[3 -2 1 | 0] R1
[0 16 1 | -2] R2
[0 0 3 | 5.5] R3 + R2/8
- Solve the triangular system starting from the last row.
After obtaining the triangular matrix, we can solve for z from the last equation, substitute back to find y from the second equation, and finally, substitute y and z to find x from the first equation.