Use a Graphing Calculator and the Method of Matrix Inverses

question 307

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) .
$\begin{array}{c|c|c|c|r}\text { Person } & \text { Green } & \text { Red } & \text { Orange } & \text { Total Cost } \\\hline \text { Bob } & 1 & 2 & 2 & \$ 29.04 \\\text { Sue } & 1 & 3 & 2 & \$ 35.91 \\\text { Fred } & 1 & 2 & 3 & \$ 34.21\end{array}$

Use this information to set up a matrix equation of the form $\mathrm { AX } = \mathrm { B }$ , 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 red :
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) \(\$ 6.50\)
• B) \(\$ 6.87\)
• C) \(\$ 6.99\)
• D) \(\$ 6.79\)

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Definitions:

Ethical Policy

A set of guidelines that outlines the principles and values governing the behavior of individuals or organizations.

Duress

Compulsion, force, or pressure applied to someone to coerce them into taking an action against their will or better judgement.

Unilateral Mistake

A situation in contract law where only one party holds an incorrect belief about a basic assumption on which a contract is based, potentially affecting the enforceability of the contract.

Mutual Mistake

A situation in a contract where all parties involved have a common but erroneous belief regarding a vital fact about the contract terms.