Solved: Write the 3 by 3 identity matrix as a combination of the other five permutation
Chapter 3, Problem 41(choose chapter or problem)
Write the 3 by 3 identity matrix as a combination of the other five permutation matrices! Then show that those five matrices are linearly independent. (Assume a combination gives CI PI + ... + Cs Ps = zero matrix, and check entries to prove Ci is zero.) The five permutations are a basis for the subspace of 3 by 3 matrices with row and column sums all equal.
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