If a and beta are the roots of the equation 1 x x2 0 then the mat...........

Mathematics (NDA) Matrices and Determinants

If a and β are the roots of the equation 1 + x + x² = 0, then the matrix product [ 1 β] [ a β ] is equal to -

[ a a] [ 1 β ]

[ 1 1 ]

[ 1 2 ]

[ −1 −1 ]

[−1 2 ]

[ 1 −1 ]

[ −1 2 ]

[ −1 −1 ]

[−1 −2 ]

α and β are the roots of given equation, so α= ω, and β = ω²

Therefore [1 β ] [ a β ] = [ a + β β + β² ]

[a a ] [ 1 β ] [ a² +a aβ + aβ ]

substituting values of α and β

=[ ω + ω² β + β² ]

[ ω² + ω 2ω² ]

=[ −1 −1 ] (as ω²+ω+1=0)

[−1 2 ]

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