5. A matrix P is said to be stochastic if the entries of P are nonnegative, and the sum of each row is one. A matrix P is said to be doubly stochastic if P is stochastic and the sum of each column is one. = (a) Suppose P1 and P2 are stochastic matrices of the same order. Consider P3 = AP1 + (1 − X)P2 for λ = [0, 1]; and P4 P₁P2. Which matrix (or matrices), P3 or P4 is (or are) stochastic? (b) Suppose P1 and P2 are doubly stochastic matrices of the same order. Consider P3 := AP₁ + (1 − λ)P2 for λ = [0, 1]; and P₁ = P₁P2. Which matrix (or P4 matrices), P3 or P4 is (or are) doubly stochastic?

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