Consider the system of linear equations - x-y-z-m x- y-z-n x-y- z-pIf -1- -2 then the system has

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Solving Equations Using Method of Substitution

Consider the ...

Question

Consider the system of linear equations
$α x + y + z = m$
$x + α y + z = n$
$x + y + α z = p$
If $α = 1, - 2$ then the system has

no solution

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infinite solutions

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unique solution

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α x + y + z = m

x + α y + z = n

x + y + α z = p

α = - 2

m + n + p \neq 0

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α

α x + y + z = α - 1, x + α y + z = α - 1, x + y + α z = α - 1

α

| α |

α x + y + z = α - 1, x + α y + z = α - 1, x + y + α z = α - 1

If the system of equations $x + α y + α^{2} z = 1, α x + y + α z = - 1, α^{2} x + α y + z = 1$ has infinitely many solutions then $1 + α + α^{2} =$

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