A sequence x[n] is specified as: \left[\begin{array}{c}x[n] \ x[n-1]]\end{array}=\left[\begin{array}{cc}1 & 1 \ 1 & 0]\end{array}^n\left[\begin{array}{c}1 \ 0]\end{array}, for n \geq 2 The initial conditions are x[0] = 1, x[1] = 1, and x[n] = 0 for n < 0. The value of x[12] is ________.

GATE Electronics and Communications (EC) 2016 Shift 1 Solved Paper

Question : 37 of 65

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A sequence x[n] is specified as:

{[\table x[n] ; x[n-1]]}={[\table 1 , 1 ; 1 , 0]}^n{[\table 1 ; 0]}

, for

n ≥ 2

The initial conditions are x[0] = 1, x[1] = 1, and x[n] = 0 for n < 0. The value of x[12] is ________.

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