Unformatted text preview: Chapter 1 ISM: Linear Algebra 5?. The second measurement in the problem tells us that 4 sparrows and 1 swallow weigh 58. 59. as much as l sparrow and 5 swallows. We will immediately interpret this as 3 sparrows
weighing the same as 4 swallows. The other measurement we use is that all the birds together weigh 1E liang. Setting $1 to he the we' t of a sparrow, and $3 to be the weight of a swallow, we ﬁnd the augmented matrix 415 representing these two
5 6: 16
equations.
1 a: 3
We reduce this to I 15' , meaning that each sparrow weighs 3 liang, and each . 19
IDLE 19
swallow weighs 1—2; liang. This problem gives us three dilferent combinations of horses that can pull exactly 4] don
up a hill. We condense the statements to ﬁt our needs, saying that, One military horse and one ordinaryr horse can pull 4D dart, two ordinary and one weak horse can pull 4] den
and one military and three weak horses can also pull 4] den. With this information, we set up our matrix: Ill ; [ll :3 , which reduces to
1 I] 3 ‘ 4e
1 U I] g
D 1 I] %
[1 ﬂ 1 $ Thus, the military horses can pull 4—? don, the ordinary horses can pull % den and the
weak horses can pull 4—,? don each. Here, let W he the depth of the well. 14 +3 —W = [I
BE +6" —W = G
Then our system heoomes 46' +3 —W = ﬂ .
5D +E —W = II]
A +BE —W = [I We transform this system into an augmented matrix, then perform a prolonged reduction 3D ...
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 Spring '09
 Derksen
 Algebra

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