作业帮关于向量和参数方程的题1.You are given four vectors in the plane,x1 and x2,b1 and b2,and you are told that there is a matrix M such that Mx1 = b1 and Mx2 = b2.Now if you are given a vector x3,how do you determine Mx3?(hint:show how to find
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关于向量和参数方程的题1.You are given four vectors in the plane,x1 and x2,b1 and b2,and you are told that there is a matrix M such that Mx1 = b1 and Mx2 = b2.Now if you are given a vector x3,how do you determine Mx3?(hint:show how to find
关于向量和参数方程的题
1.You are given four vectors in the plane,x1 and x2,b1 and b2,and you are told that there is a matrix M such that Mx1 = b1 and Mx2 = b2.Now if you are given a vector x3,how do you determine Mx3?(hint:show how to find out what M is from the data,and then apply it to x3).
2.Write down the parametric equation of the points on a line that passes through two points in space,p1 and p2; now write down the parametric equation of the points on a plane that contains these two points and a third point,p3.Show how to use these parametric equations and some inequalities on the parameters to specify (a) all the points on the line that lie between p1 and p2 and (b) all the points on the triangle whose vertices are p1,p2 and p3.
补充个自己的翻译吧 我自己都看不懂 不对的话麻烦自己理解下吧
1.平面上有4个向量x1,x2和b1,b2，有一个矩阵M使得Mx1=b1,Mx2=b2，现在有向量x3，问怎样确定Mx3？（提示：说明如何找出数据中M并把它应用到X3中）
2.写出一条过空间两点P1,P2的直线的参数方程，然后写出平面上一条直线过这两点并且过第三个点P3，写出如何用这些参数方程和未知参量来描述（a）直线上所有位于点P1,P1之间的点（b）三角形中所有点顶点为P1,P2,P3的点
关于向量和参数方程的题1.You are given four vectors in the plane,x1 and x2,b1 and b2,and you are told that there is a matrix M such that Mx1 = b1 and Mx2 = b2.Now if you are given a vector x3,how do you determine Mx3?(hint:show how to find
首先,这个矩阵M是个2*2的矩阵,你先用X1、X2组成一个矩阵叫X,是个2*2的矩阵,用b1、b2组成另外一个矩阵叫B,也是个2*2的矩阵.
那么有MX=B,这是个方程组,可以解出矩阵M
然后把矩阵M代入到X3里面去就可以了.
这是大学《线性代数》（或者叫《高等代数》）教的东西.
假设P1、P2的横纵坐标分别是X1、Y1,X2、Y2可以列出一个方程组：
X=aT
Y=T+b,
把两个坐标代进去,可以分别解出a、b
那么,a=(x1-x2)/(y1-y2)
b=(x1y2-x2y1)/(x1-x2)
那么,这就是直线的参数方程,参数是T.
然后,你可以分别解出P1、P2对应的参数T1、T2,
在两点之间,等价于,参数T在T1、T2之间.
第二个问题看不懂.