Book edition 5th

Author(s) Otto Bretscher

Pages 442 pages

ISBN 9780321796974

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Short Answer

Five cows and two sheep together cost 10 liang of silver. Two cows and five sheep together cost eight liang of silver. What is the cost of a cow and a sheep, respectively? (Nine Chapters, Chapter 8, Problem 7)

$\frac{34}{21}$ liang is the cost of a cow and $\frac{20}{21}$ liang is the cost of a sheep.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Represent the cost of cows and sheep in terms of a system of equations.

The cost of a cow and a sheep can be found using the augmented matrix.

$5$ cows and $2$ sheep together cost $10$ liang of silver.

$5 C + 3 S = 10 ...... (1)$

$2$ cows and $5$ sheep together cost $8$ liang of silver.

$2 C + 5 S = 8 ...... (2)$

Consider the equations (1) and (2). The system of equations is,

$| \begin{array}{l} 5 C + 3 S = 10 \\ 2 C + 5 S = 8 \end{array} |$

Represent the above equations in terms of a matrix.

$| \begin{matrix} 5 & 3 & 10 \\ 2 & 5 & 8 \end{matrix} |$

Step 2: Perform the row operations on the matrix

Consider the obtained matrix, now reduce it into row echelon form.

$rref | \begin{matrix} 5 & 3 & 10 \\ 2 & 5 & 8 \end{matrix} | \to | \begin{matrix} 1 & 0 & \frac{34}{21} \\ 0 & 1 & \frac{20}{21} \end{matrix} |$

The values are, $C = \frac{34}{21}, S = \frac{20}{21}$ .

Hence, $\frac{34}{21}$ liang is the cost of a cow and $\frac{20}{21}$ liang is the cost of a sheep.

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Linear Algebra With Applications

Answers without the blur.

Short Answer

Five cows and two sheep together cost 10 liang of silver. Two cows and five sheep together cost eight liang of silver. What is the cost of a cow and a sheep, respectively? (Nine Chapters, Chapter 8, Problem 7)

Step by Step Solution

Step 1: Represent the cost of cows and sheep in terms of a system of equations.

Step 2: Perform the row operations on the matrix

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Linear Algebra With Applications

Answers without the blur.

Short Answer

Five cows and two sheep together cost 10 liang of silver. Two cows and five sheep together cost eight liang of silver. What is the cost of a cow and a sheep, respectively? (Nine Chapters, Chapter 8, Problem 7)

Step by Step Solution

Step 1: Represent the cost of cows and sheep in terms of a system of equations.

Step 2: Perform the row operations on the matrix

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