Short Answer

Students are buying books for the new semester. Brigitte buys the German grammar book and the German novel, Die Leiden des jungen Werther, for $Є 64$ in total. Claude spends $Є 98$ on the linear algebra text and the German grammar book, while Denise buys the linear algebra text and Werther, for $Є 76$ . How much does each of the three books cost?

The German grammar book, the German novel – Die Leiden des Jungen Werther and the linear algebra text cost, $Є 43, Є 21$ and $Є 55$ respectively.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Represent the money spent by Brigitte, Claude, and Denise in terms of a system of equations.

The cost of each book can be found using the augmented matrix.

The system of equations is,

$|\begin{matrix} G + W = 64 \\ G + L = 98 \\ W + L = 76 \end{matrix}|$

Represent the above equations in terms of a matrix.

$|\begin{matrix} 1 & 1 & 0 & 64 \\ 1 & 0 & 1 & 98 \\ 0 & 1 & 1 & 76 \end{matrix}|$

Step 2: Perform the row operations on the matrix.

Consider the obtained matrix and reduce it into row echelon form:

$rref | \begin{matrix} 1 & 1 & 0 & 64 \\ 1 & 0 & 1 & 98 \\ 0 & 1 & 1 & 76 \end{matrix} | \approx | \begin{matrix} 1 & 0 & 0 & 43 \\ 0 & 1 & 0 & 21 \\ 0 & 0 & 1 & 55 \end{matrix} |$

The values are, $G = Є 43, W = Є 21, L = Є 55$ .

Hence, the German grammar book, the German novel – Die Leiden des Jungen Werther and the linear algebra text cost, $Є 43, Є 21$ and $Є 55$ respectively.

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Linear Algebra With Applications

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Step 1: Represent the money spent by Brigitte, Claude, and Denise in terms of a system of equations.

Step 2: Perform the row operations on the matrix.

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Step by Step Solution

Step 1: Represent the money spent by Brigitte, Claude, and Denise in terms of a system of equations.

Step 2: Perform the row operations on the matrix.

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