推 et548548 :t這個未知數代表捨麼?? 10/05 22:13
→ lenux :代表答案會有無窮多組解 隨t的值而變 10/05 22:20
→ lenux :是因為在高斯消去法的過程中沒有辦法解出所有X的值 10/05 22:20
※ 引述《et548548 (John小毛)》之銘言：
: 上次被資管同學考倒= =，完全看不懂這啥問題
: 不知道是不是分析這一類的問題，我怕我問錯!
: The accompanying sketch represents a maze of one-way streets in a city in the
: United States. The traffic volume through certain blocks during an hour has
: been measured. Suppose that the vehicles leaving the area during this hour
: were exactly the same as those entering it.
: http://www.badongo.com/cn/pic/7344593
: What can you say about the traffic volume at the four locations indicated by
: a question mark? Can you figure out exactly how much traffic there was on
: each block? If not, describe one possible scenario. For each of the four
: locations, find the highest and the lowest possible traffic volume
這應該屬於線性代數中的網路分析 Network Analysis (或是交通流量 Traffic Flow)
它的法則是：在一個節點(Junction)中，流入等於流出：flow in = flow out)
將剛剛的圖整理成...
400 100
↑ │
│ ↓
300─→J1─→J2─→250
↑ X1 ↑
X4│ │X2
320←─J4←─J3←─120
↑ X3 ↑
│ │
300 150
對於 J1 這個節點來說： X4+300 = X1+400 以此類推可得到...
J1: X4+300 = 400+X1
J2: X1+X2+100 = 250
J3: 120+150 = X2+X3
J4: X3+300 = 320+X4
整理一下後
X4-X1 = 100
X1+X2 = 150
X2+X3 = 270
X3-X4 = 20
再用矩陣的方式表達
┌ -1 0 0 1 ┐┌ X1 ┐ ┌ 100 ┐
│ 1 1 0 0 ││ X2 │ │ 150 │
│ 0 1 1 0 ││ X3 │=│ 270 │
└ 0 0 1-1 ┘└ X4 ┘ └ 20 ┘
接下來就請自己用高斯消去法計算囉
答案必須使用參數表達法：
令 X4 = t
X3 = 20+t
X2 = 250-t
X1 = t+100
有錯請糾正～謝謝
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