Exercise 3.4.8: Find the general solution of x₁ = x₁ - 2x2, x2 = 2x₁ + x2 using the eigenvalue method. Do not use complex exponentials in your solution.

the price of a stock drops $3 each day for 7 days. The stock was worth $50 before the price began dropping. What is the price of the stock after the price dropped in price.

A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chessboard. On the second square, the King would place two grains of​ wheat, on the third​ square, four grains of​ wheat, and on the fourth square eight grains of wheat. If the amount of wheat is doubled in this way on each of the remaining​ squares, how many grains of wheat should be placed on a square 16​? Also, find the total number of grains of wheat on the board at this time and their total weight in pounds.​ (Assume that each grain of wheat weighs​ 1/7000 pounds.)

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