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Examine the consistency of the system of...

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

Text Solution

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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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