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GATE EC 2016 Set 1 — Question 37

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NAT+2 / -0MediumMatrix AlgebraLinear AlgebraEngineering MathematicsEigenvalues & Eigenvectors

Engineering Mathematics → Linear Algebra → Eigenvalues & Eigenvectors

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A sequence x[n]x[n] is specified as[x[n]x[n−1]]=[1110]n[10], for n≥2.\begin{bmatrix} x[n] \\ x[n-1] \end{bmatrix} = \begin{bmatrix} 1 & 1 \\ 1 & 0 \end{bmatrix}^n \begin{bmatrix} 1 \\ 0 \end{bmatrix}, \text{ for } n \geq 2.The initial conditions are x[0]=1,x[1]=1x[0] = 1, x[1] = 1, and x[n]=0x[n] = 0 for n<0n < 0. The value of x[12]x[12] is ______
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