章节大纲

  • Chapter Project: Matrices
    ::分章项目:

    In Gotham City, avenues run north-south and streets run east-west. Many of the roads alternate direction and are one-way streets. In this example, Avenue A is west of Avenue B and they are parallel. Both are perpendicular to 2nd  Street and 3rd  Street (which are parallel to each other with 2nd Street north of 3rd Street). Avenue A traffic runs north only, and Avenue B traffic runs south only. Cars on 2nd Street can only drive west. Cars on 3rd Street can only drive east. City planners have requested data to improve the lane use and light timing. Here are the data provided for these four intersections:
    ::在哥谭市,通向南北,街道为东-西,许多道路交错方向,是单行街道,例如,A大道位于B大道以西,与B大道平行,与第二街和第三街相连(与第三街以北第二街平行),A大道仅向北,B大道仅向南,第二街的汽车只能向西行驶,第三街的汽车只能向东行驶。城市规划者要求获得数据,以改善车道的使用和灯光时间。

    • Four hundred cars enter the intersection of Avenue A and 3rd Street from the south on Avenue A.
      ::400辆汽车从A大道以南进入A大道A和3街交汇处。
    • Two hundred cars exit the intersection of Avenue A and 2nd Street headed north on Avenue A.
      ::200辆汽车从A大道和2街大道交叉口出口,向北走A大道。
    • Nine hundred cars enter the intersection of Avenue B and 2nd Street headed south on Avenue B.
      ::九百辆汽车进入B大道和2街交叉路口,向B大道以南行驶。
    • Two hundred cars exit the intersection of Avenue B and 3rd Street on Avenue B headed south.
      ::200辆汽车从B大道交叉口和B大道3街交叉口向南行驶。
    • Five hundred cars enter the intersection of Avenue B and 2nd Street headed west on 2nd Street.
      ::五百辆汽车进入B大道和2街交叉口,向西行驶在2街。
    • Seven hundred cars exit the intersection of Avenue A and 2nd Street headed west on 2nd Street.
      ::七百辆汽车从A大道和2街交叉口 向西驶去第二街
    • Five hundred cars enter the intersection of Avenue A and 3rd Street headed east on 3rd Street.
      ::五百辆汽车进入A大道和三街交叉路口 向东行驶在三街
    • Three hundred cars exit the intersection of Avenue B and 3rd Street headed east on 3rd Street.
      ::三百辆汽车从B大道和三街交叉口 向东行驶到三街

    Project Steps:
    ::项目步骤:

    • Create a diagram that models the situation described.
      ::创建用于模拟所描述情况的图表。
    • Label the number of cars that exit at each intersection with the variables  c 1 , c 2 , c 3 , c 4 .
      ::标记每次离开的汽车数量与变量c1、c2、c3、c4的交叉点。
    • Create four equations to represent the traffic in and out of the intersections.
      ::创建四个方程式以代表交叉点的进出流量 。
    • Create an augmented matrix to represent the traffic patterns.
      ::创建用于代表交通模式的扩展矩阵。
    • Determine the restrictions on the variables. 
      ::确定变量的限制。
    • Does the system have a unique solution? Can you determine at least one solution? Explain.
      ::系统是否有独特的解决方案? 您能确定至少一个解决方案吗? 解释一下 。