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Linear Algebra With Applications
Found in: Page 23
Linear Algebra With Applications

Linear Algebra With Applications

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)

3421 liang is the cost of a cow and2021 liang is the cost of a sheep.

See the step by step solution

Step by Step Solution

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 2sheep together cost10 liang of silver.

5C+3S=10     ......(1)

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

2C+5S=8     ......(2)

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


Represent the above equations in terms of a matrix.


Step 2: Perform the row operations on the matrix

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


The values are, C=3421,S=2021 .

Hence, 3421 liang is the cost of a cow and 2021liang is the cost of a sheep.

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