Let A = (aij ) be the 23 × 23 real matrix defined by aij = 23 for all i, j. Let LA : R 23 → R 23 denote the linear operator defined by LA(x) = Ax. (a) Show that the vector v = (1, 1, . . . , 1) ∈ R 23 is an eigenvector of A. (b) Show that A is diagonalizable, and describe a basis β such that [LA]β is diagonal

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