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Matrices and Determinants question

2014 · Shift 0 · Q32

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JEE Main
Mathematics
Matrices and Determinants
2014 · Shift 0 · Q32

Matrices and Determinants question

2014 · Shift 0 · Q32

JEE MainMathematicsMatrices and DeterminantsMCQ+4 / −1

If

\alpha ,\beta e 0,

and

f\left( n \right) = {\alpha ^n} + {\beta ^n}

and

\left| {\begin{matrix} 3 & {1 + f\left( 1 \right)} & {1 + f\left( 2 \right)} \\ {1 + f\left( 1 \right)} & {1 + f\left( 2 \right)} & {1 + f\left( 3 \right)} \\ {1 + f\left( 2 \right)} & {1 + f\left( 3 \right)} & {1 + f\left( 4 \right)} \\ \end{matrix} } \right|

= K{\left( {1 - \alpha } \right)^2}{\left( {1 - \beta } \right)^2}{\left( {\alpha - \beta } \right)^2},

then

K

is equal to :

A
$1$
B
$-1$
C
$\alpha \beta$
D
${1 \over {\alpha \beta }}$

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