Bill is trying to plan a meal to meet specific nutritional goals. He wants to prepare a meal containing rice, tofu. and peanuts that will provide 193 grams of carbohydrates, 258 grams of fat, and 15:9I grams of protein. He knows that each cup of rice provides 45 grams of carbohydrates. 0 grams of fat. and 3 grams of protein. Each cup of tofu provides ? grams of carbohydrates, '13 grams of fat, and 16 grams of protein. Finally, each cup of peanuts provides 1'} grams of carbohydrates, 1'3 grams of fat. and 35 grams of protein. HOW manyI cups of rice. tofu, and peanuts should he eat? You wish to make a snack mixes from peanuts and almonds to sell in your health-food store. Mix A is half peanuts and half almonds. Mix B is one fourth peanuts and three-fourths almonds. If you have 15 pounds of peanuts and 2D pounds of almonds, how many pounds of each mix should you make to exactly use all of your ingredients? Quantity of Mix A =I I pounds Quantity of Mix B = I I pounds You have 510,000 to split into two investments: a highyield account that earns 5% annual interest. and a lowrisk account that earns 19:: annual interest. You would like to earn a total of S400 interest in a year. How much money should you invest in each account? Answer this question by setting up a system of equations. representing it as a matrix equation and solving that matrix equation using an inverse matrix. Investment in high-yield account = l dollars Investment in low-risk account = I |dollars NOTE: There is a small error at the end of the video above. The final vector should be , and the final value for y should be 1 (not 3). Consider the system of equations 2x + y = 3 3x + 2y = 1. This system can be represented as a matrix equation AX + B with A = and B = The inverse of the coefficient matrix is If we multiply both sides of the matrix equation AX = B by A-1, we get X = A-1B, where A B =The inverse of the coefficient matrix is A- If we multiply both sides of the matrix equation AX = B by A-1, we get X = A-1B, where A B = Therefore, the solution of this system of equations is T= and y