The value of the determinant $\left| {\begin{array}{*{20}{c}} {1 - {\rm{\alpha }}}&{{\rm{\alpha }} - {{\rm{\alpha }}^2}}&{{{\rm{\alpha }}^2}}\ {1 - {\rm{\beta }}}&{{\rm{\beta }} - {{\rm{\beta }}^2}}&{{{\rm{\beta }}^2}}\ {1 - {\rm{\gamma }}}&{{\rm{\gamma }} - {{\rm{\gamma }}^2}}&{{{\rm{\gamma }}^2}} \end{array}} \right|$ is equal to

Question

The value of the determinant $\left| {\begin{array}{*{20}{c}} {1 - {\rm{\alpha }}}&{{\rm{\alpha }} - {{\rm{\alpha }}^2}}&{{{\rm{\alpha }}^2}}\ {1 - {\rm{\beta }}}&{{\rm{\beta }} - {{\rm{\beta }}^2}}&{{{\rm{\beta }}^2}}\ {1 - {\rm{\gamma }}}&{{\rm{\gamma }} - {{\rm{\gamma }}^2}}&{{{\rm{\gamma }}^2}} \end{array}} \right|$ is equal to

TuteeHUB · Accepted Answer

(α - β)(β - γ)(γ - α)(α + β + γ)

TuteeHUB · Answer

(α - β)(β - γ)(α - γ)

TuteeHUB · Answer

(α - β)(β - γ)(γ - α)

1.	The value of the determinant \(\left\| {\begin{array}{*{20}{c}} {1 - {\rm{\alpha }}}&{{\rm{\alpha }} - {{\rm{\alpha }}^2}}&{{{\rm{\alpha }}^2}}\\ {1 - {\rm{\beta }}}&{{\rm{\beta }} - {{\rm{\beta }}^2}}&{{{\rm{\beta }}^2}}\\ {1 - {\rm{\gamma }}}&{{\rm{\gamma }} - {{\rm{\gamma }}^2}}&{{{\rm{\gamma }}^2}} \end{array}} \right\|\) is equal to
A.	(α - β)(β - γ)(α - γ)
B.	(α - β)(β - γ)(γ - α)
C.	(α - β)(β - γ)(γ - α)(α + β + γ)
D.	0
Answer» C. (α - β)(β - γ)(γ - α)(α + β + γ)

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