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Found in: Page 23

### Linear Algebra With Applications

Book edition 5th
Author(s) Otto Bretscher
Pages 442 pages
ISBN 9780321796974

# Students are buying books for the new semester. Brigitte buys the German grammar book and the German novel, Die Leiden des jungen Werther, for${\mathbit{Є}}{\mathbf{64}}$ in total. Claude spends ${\mathbit{Є}}{\mathbf{98}}$ on the linear algebra text and the German grammar book, while Denise buys the linear algebra text and Werther, for ${\mathbit{Є}}{\mathbf{76}}$. 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, $Є43,Є21$ and$Є55$ respectively.

See the step by step solution

## 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,

$\left|\begin{array}{c}G+W=64\\ G+L=98\\ W+L=76\end{array}\right|$

Represent the above equations in terms of a matrix.

$\left|\begin{array}{cccc}1& 1& 0& 64\\ 1& 0& 1& 98\\ 0& 1& 1& 76\end{array}\right|$

## Step 2: Perform the row operations on the matrix.

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

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

The values are, $G=Є43,W=Є21,L=Є55$ .

Hence, the German grammar book, the German novel – Die Leiden des Jungen Werther and the linear algebra text cost, $Є43,Є21$ and $Є55$respectively.