Question

Examine the consistency of the following system of equations. If it is consistent then solve the same. 

4x + 3y + 6z = 25, x + 5y + 7z = 13, 2x + 9y + z = 1

Answer 1

The augmented matrix is

The last equivalent matrix is in the echelon form. It has three non-zero rows.

∴ The given system is consistent and has a unique solution 

4x + 3y + 6z = 25 …… (1)

∴ The unique solution is x = 4, y = -1, z = 2.