#### Question

Examine the consistency of the system of equations.

*x* +* y *+ *z* = 1

2*x* + 3*y* + 2*z* = 2

*ax* + *ay* + 2*az* = 4

#### Solution

The given system of equations is:

*x* +* y *+ *z* = 1

2*x* + 3*y* + 2*z* = 2

*ax* + *ay* + 2*az* = 4

This system of equations can be written in the form *AX* = *B*, where

∴ *A* is non-singular.

Therefore, *A*^{−1} exists.

Hence, the given system of equations is consistent.

Is there an error in this question or solution?

Solution Examine the Consistency of the System of Equations.X + Y + Z = 1 2x + 3y + 2z = 2 Ax + Ay + 2az = 4 Concept: Applications of Determinants and Matrices.