Examine the consistency of the system of equations
`5x -y + 4z = 5," "``2x + 3y + 5z = 2," "``5x -2y + 6z = 1`

Explanation

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

`A = [[5,-1,4],[2,3,5],[5,-2,6]]`

`X = [[x],[y],[z]]`

`B = [[5],[2],[-1]]`

`=>AX = B`

`=>A^-1AX = A^-1B`

`=>X = A^-1B`

Therefore, if `A^1` exists, we will have a unique solution for these linear equations.

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