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Linear AlgebraSuperchallengeRow Reduction & Rank

Row Reduction & Rank · Superchallenge problem

The 9999 unknowns x1,x2,…,x99x_1, x_2, \ldots, x_{99} satisfy the tridiagonal system

−xk−1+2xk−xk+1=k(k=1,2,…,99),-x_{k-1} + 2x_k - x_{k+1} = k \qquad (k = 1, 2, \ldots, 99),

where x0=x100=0x_0 = x_{100} = 0. Find x50x_{50}.