Q2 of 127 Page 136

Examine the consistency of the system of equations.

2x – y = 5


x + y = 4

The given system of equations is:

2x - y = 5


x + y = 4


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



Now |A| = 2(1)-1(-1) = 3 ≠ 0.


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


So, The system of equations will be consistent.


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If A is an invertible matrix of order 2, then det (A–1) is equal to

 1

Examine the consistency of the system of equations.

x + 2y = 2


2x + 3y = 3

 3

Examine the consistency of the system of equations.

x + 3y = 5


2x + 6y = 8

 4

Examine the consistency of the system of equations.

x + y + z = 1


2x + 3y + 2z = 2


ax + ay + 2az = 4