Question

Examine the consistency of the system of equations.
5x−y+4z=5,
2x+3y+5z=2,
5x−2y+6z=−1

Answer 1

The given system of equations is:
5x − y + 4z = 5
2x + 3y + 5z = 2
5x − 2y + 6z = −1
This system of equations can be written in the form of AX = B, where

A=$\begin{bmatrix}5&-1&4\\\2&3&5\\\5&-2&6\end{bmatrix}$,X=$\begin{bmatrix}x\\\y\\\z\end{bmatrix}$and B=$\begin{bmatrix}5\\\2\\\\-1\end{bmatrix}$

Now,
IAI=5(18+10)+1(12-25)+4(-4-15)
=5(28)+1(-13)+4(-4-15)
=140-13-76
=51$\neq$ 0
∴ A is non-singular.
Therefore, A-1 exists.

Hence, the given system of equations is consistent.