math111_logo Row Operation


Exercise Try different row operations on the augmented matrix in this example. Then derive the same conclusion.

Exercise Solve systems of linear equations.

x1 - x2 + 3x3 = 3
3x1 + x2 + x3 = 5
x1 + x2 - x3 = 1
2x1 - 3x2 - x3 = 3
x1 + x2 + 2x3 = -1
x1 + 2x2 = 3
4x1 + 5x2 = 6
7x1 + 8x2 = 9
x1 + 3x2 + 2x3   + x5 = 0
- x1 - x2 - x3 + x4   = 1
  4x2 + 2x3 + 4x4 + 3x5 = 3
x1 + 3x2 + 2x3 - 2x4   = 0
x1 + 3x2 + 2x3   + x5 = 0
- x1 - x2 - x3 + x4   = 1
  4x2 + 2x3 + 4x4 + 3x5 = 2
x1 + 3x2 + 2x3 - 2x4   = 0

Answer

Exercise Prove that if a matrix A can be changed to a matrix B by row operations, then the matrix B can also be changed to a matrix A by row operations.

Answer