Use a Graphing Calculator and the Method of Matrix Inverses

question 358

Multiple Choice

Use a graphing calculator and the method of matrix inverses to Give five decimal places, if necessary.
-A bookstore is having a sale. All books included in the sale have a colored sticker on them to indicate the sale price. There are green stickers, red stickers, and orange stickers. Bob, Sue, and Fred each make purchases of books that are on sale. Each row of the table gives information about the numbers of book purchases and the total cost of the purchase (before taxes) .
$\begin{array}{c|c|c|c|r}\text { Person } & \text { Green } & \text { Red } & \text { Orange } & \text { Total Cost } \\\hline \text { Bob } & 1 & 2 & 2 & \$ 28.98 \\\text { Sue } & 1 & 3 & 2 & \$ 35.85 \\\text { Fred } & 1 & 2 & 3 & \$ 34.12\end{array}$

Use this information to set up a matrix equation of the form $A X = B$ , which can be solved to determ: the price for each type of sale book. Solve this matrix equation to find the price of a book with a gree sticker.
Use the fact that for $A = \left[ \begin{array} { l l l } 1 & 2 & 2 \\ 1 & 3 & 2 \\ 1 & 2 & 3 \end{array} \right] , A ^ { - 1 } = \left[ \begin{array} { r r r } 5 & - 2 & - 2 \\ - 1 & 1 & 0 \\ - 1 & 0 & 1 \end{array} \right]$ .

• A) \(\$ 4.96\)
• B) \(\$ 4.91\)
• C) \(\$ 4.99\)
• D) \(\$ 4.89\)

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Definitions:

Negligence

An unintentional, careless act or omission that causes injury to another person or his property.

Sale of Goods Act

Legislation governing the sale of goods, providing rights and obligations for both buyers and sellers.

Goods and Services

Tangible products and intangible activities offered to consumers or businesses in the marketplace.

Caveat Emptor

“Let the buyer beware”; a principle that the purchaser must examine, judge, and test for herself.