#### Question

Examine the consistency of the system of equations.

5*x* −* y *+ 4*z* = 5

2*x* + 3*y* + 5*z* = 2

5*x* − 2*y* + 6*z* = −1

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#### Solution

The given system of equations is:

5*x* −* y *+ 4*z* = 5

2*x* + 3*y* + 5*z* = 2

5*x* − 2*y* + 6*z* = −1

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

∴ *A* is non-singular.

Therefore, *A*^{−1} exists.

Hence, the given system of equations is consistent.

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#### Reference Material

Solution for question: Examine the Consistency of the System of Equations. 5x − Y + 4z = 5 2x + 3y + 5z = 2 5x − 2y + 6z = −1 concept: Applications of Determinants and Matrices. For the courses CBSE (Arts), CBSE (Commerce), CBSE (Science)