2. (15 points) Let A be a n x n matrix such that a b b b a b (HS) where a, b E R. (a) (5 points) Prove, by direct comput

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2 15 Points Let A Be A N X N Matrix Such That A B B B A B Hs Where A B E R A 5 Points Prove By Direct Comput 1 (114.59 KiB) Viewed 26 times

2. (15 points) Let A be a n x n matrix such that a b b b a b (HS) where a, b E R. (a) (5 points) Prove, by direct computation, that the following relation holds. la b b b a- b Võ a b a b võ HIC-JO- Vo VB). b b a (b) (10 points) Hence show that |A| without proof (a · b)n−¹[a + (n − 1)b]. You can use the following result for any invertible matrix A and column vectors of appropriate sizes u, v, we have det (A + uvT) = (1 + v™ A−¹u)det(A). This result is implied by the Sherman-Morrison-Woodbury formula.