(a) Let A € R™×n be a tridiagonal matrix, i.e. bị Ci ... az b2 c2 0 a3 b3 ... ... A = 0 0 0 0 0 0 bn-1 Cn-1 ... an ... Devise an algorithm for computing leading principal minors of A whose cost : linear with respect to n. (b) Is the matrix 1 -1 0 ... -1 -1 ... -1 2 ... 2 -1 ... -1 2 ... positive definite? Give a precise argument. *.* N

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