Question

Show that the equations 2x + 6y + 11 = 0, 6x + 20y - 6z + 3 = 0 and 6y - 18z + 1 = 0 are not consistent.

Answer 1

So, the system is inconsistent.

Alternate method: The given system of equations is equivalent to the single matrix equation:

We shall reduce the coefficient matrix A to triangular form by E-row operations on it and apply the same operations on the right-hand side, i.e. on the matrix B.

Performing R₂ → R₂ - 3R₁, we have

Performing R₃ → R₃ - 3R₂, we have

The last equation of this system is 0x + 0y + 0z = -91. This shows that the given system is not consistent.