**Problem Statement:** The payoff matrix and strategies $ P $ and $ Q $ (for the row and column players, respectively) are given. Find the expected payoff $ E $ of each game. (Round your answer to two decimal places.)**Given Data:**- Payoff Matrix: \[\begin{bmatrix}3 & 1 \\-4 & 2 \end{bmatrix}\]- Strategy $ P $ for the row player:\[P = \begin{bmatrix}\frac{1}{4} & \frac{3}{5}\end{bmatrix}\]- Strategy $ Q $ for the column player:\[Q = \begin{bmatrix}\frac{4}{7} \\\frac{3}{7} \end{bmatrix}\]**Expected Payoff Calculation:**$ E = $(Enter your calculated value here.)**Instruction:**Click "Show My Work" if you would like to provide your steps and calculations (Optional).---In the problem presented, we have two players with respective strategies $ P $ and $ Q $. The goal is to calculate the expected payoff $ E $ for one game scenario using the provided payoff matrix and strategies. The calculations should be rounded to two decimal places.Note: This exercise will involve matrix multiplication to compute the expected payoff. Ensure your answers are accurate by following the matrix multiplication rules carefully. ---**Optional Section: Show My Work**- Here, input the detailed steps for matrix multiplication and how to derive the expected payoff $ E $.

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

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The payoff matrix and strategies P and Q (for the row and column players, respectively) are given. Find the expected payoff E of each game. (Round your answer to two decimal places.) -- Q = E = P Show My Work (Optional)?