1. For breakfast, Yoko had cereal, a banana, a cup of milk and a slice of toast. She recorded the nutritional information in her food journal: cereal has 165 calories, 33 g of carbohydrate, 3 g of fat, and no cholesterol; a banana has 120 calories, 26 g of carbohydrate, no fat, and no cholesterol; milk has 120 calories, 11 g of carbohydrate, 5 g of fat, and 15 g cholesterol; and toast has 125 calories, 14 g of carbohydrate, 6 g of fat, and 18 g cholesterol. Display this nutritional information in a matrix N whose rows represent the foods and columns represent calories, carbs, fat, and cholesterol in that order. a.If Yoko has the same thing five days a week, create a matrix to represent the quantity of her weekly order. b.Use matrix multiplication to find how many calories, carbohydrates, fat and cholesterol Yoko takes in for breakfast.

2. Suppose Sally goes to the store to buy a bag of dog food for $22.95, two candy bars at $1.25 each, a box of cereal for $4.95, and three cartons of soda for $2.95 each. a. Create a quantity matrix Q and price matrix P for the purchases. b. Use matrix multiplication to find the total cost QP of Terri’s purchases.

3. Let matrix:M =111 Calculate M 2, M 3, and M 4. Do you notice a pattern?

4. Identity Matrix 4 7a b 4 7 x = -5 2c d -5 2 So what do you think the identity matrix means? What do you think the identity matrix for a two by two matrix?

5. Identity Matrix When dealing with matrix computation, it is important to understand the identity matrix. Think of the identity matrix as the multiplicative identity of square matrices, or the one of square matrices. Any square matrix multiplied by the identity matrix of equal dimensions on the left or the right doesn't change.

6. Suppose you invest $25,000 in a 12-month CD at 3.2% (annual yield), deposit $37,000 in your savings account at 4.5%, and $22,500 in government bonds at 6.2% annual interest. What will the value of your investments be after one year? a. Write a row matrix V that shows the current value of each investment. b. Write a column matrix Y that shows the yield of each investment. c. Use matrix multiplication to find the value of your earnings after one year

7. Suppose the cost of ordering pizzas with two toppings and salads with a choice of two dressings at 3 pizza restaurants are shown by the chart on the next page. And suppose for a pizza party, you decide to order 5 two-topping pizzas and 3 salads with two dressings….can you calculate the total cost for each shop using matrix multiplication? Vinny’sTony’sSal’s Pizza$11.25$11.96$11.90 Salad$3.69$4.34$4.35

8. Kate borrows $10,000…. some from her friend Joe at 8% annual interest, twice as much as that from her aunt Susie at 9%, and the remainder from her insurance company at 5%. She pays a total of $ 830 interest for the first year. How much did she borrow from each source?

9. The following matrix consists of a shoe store’s inventory of flip flops, clogs, and sandals in sizes small, medium, and large: If the unit prices of the shoes are $15, $20 and $25 respectively regardless of the size, how much is the store inventory worth retail? If retail is 55% above wholesale, how much does the store have invested in the wholesale inventory? SmallMediumLarge Flip Flops203515 Clogs154224 Sandals183822