Sudoku is a popular puzzle involving matrices. In this puzzle one is given some of the

Chapter 7, Problem 25

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Sudoku is a popular puzzle involving matrices. In this puzzle one is given some of the entries of a 9 9 matrix A and asked to fill in the missing entries. The matrix A has block structure A = A11 A12 A13 A21 A22 A23 A31 A32 A33 where each submatrix Aij is 3 3. The rules of the puzzle are that each row, each column, and each of the submatrices of A must be made up of all of the integers 1 through 9. We will refer to such a matrix as a sudoku matrix. Show that if A is a sudoku matrix, then = 45 is its dominant eigenvalue.

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