Q4 of 127 Page 136

Examine the consistency of the system of equations.

x + y + z = 1


2x + 3y + 2z = 2


ax + ay + 2az = 4

The given system of equations is:

x + y + z = 1


2x + 3y + 2z = 2


ax + ay + 2az = 4


The given system of equations can be written in the form of AX = B, where



Now |A| = 1(6a-2a)-1(4a-2a) +1(2a-3a) = a ≠ 0


∴ A is a non-singular matrix and hence A-1 exists.


So the system of equations will be consistent.


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